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Probability-and-statistics/1205907 (2024-01-31 16:11:36): Flaws in plate glass used for large office buildings occur randomly at an average of 1 per 10 square feet.
PLEASE USE 4 DECIMAL PLACES IN THE ANSWERS.
Question content area bottom
Part 1
a) What is the probability that a 6 ft. by 10 ft. sheet of this type of glass will contain less than 2 flaws?
The probability that a 6 ft. by 10 ft. sheet of this type of glass will contain less than 2 flaws is
enter your response here.
b) What is the probability that a 6 ft. by 10 ft. sheet of this type of glass will contain at least 1 flaw?
The probability that a 6 ft. by 10 ft. sheet of this type of glass will contain at least 1 flaw is
enter your response here.
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Linear_Equations_And_Systems_Word_Problems/1205785 (2024-01-24 10:30:42): A factory makes three products called Spring, Autumn, and Winter, from three materials containing Cotton, Wool and Silk. The following table provides details on the sales price, production cost and purchase cost per ton of products and materials respectively.
Sales price
Spring $60
Autumn $55
Winter $60
Production cost
Spring $5
Autumn $3
Winter $5
Purchase price
Cotton $30
Wool $45
Silk $50
The maximal demand (in tons) for each product, the minimum cotton and wool propor- tion in each product is as follows:
Demand
Spring 3300
Autumn 3600
Winter 4000
min Cotton proportion
Spring 55%
Autumn 45%
Winter 30%
min Wool proportion
Spring 30%
Autumn 40%
Winter 50%
a) Formulate an LP model for the factory that maximises the profit, while satisfying the demand and the cotton and wool proportion constraints. There is no penalty for the shortage.
b) Find the optimal profit and optimal values of the decision variables.
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Linear_Equations_And_Systems_Word_Problems/1205784 (2024-01-24 10:21:56): A factory makes three products called Spring, Autumn, and Winter, from three materials containing Cotton, Wool and Silk. The following table provides details on the sales price, production cost and purchase cost per ton of products and materials respectively.
Sales price Production cost Purchase price
Spring $60 $5 Cotton $30
Autumn $55 $3 Wool $45
Winter $60 $5 Silk $50
The maximal demand (in tons) for each product, the minimum cotton and wool propor- tion in each product is as follows:
Demand min Cotton proportion min Wool proportion
Spring 3300 55% 30%
Autumn 3600 45% 40%
Winter 4000 30% 50%
a) Formulate an LP model for the factory that maximises the profit, while satisfying the demand and the cotton and wool proportion constraints. There is no penalty for the shortage.
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Probability-and-statistics/1205781 (2024-01-24 08:23:08): In a certain city, the distribution of the first-and second - born children of two - child families by gender is shown below.
First born Second born Total
Female Male
Female 530 510 1040
Male 480 430 910
TOTAL 1010 940 1950
a.) A family in this city with two children has a male first- born. What is the probability that its second- born is female? (5 points)
b.) What is the probability that a family with two children selected at random in this city has children of same gender? (5 points)
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Complex_Numbers/1205713 (2024-01-20 14:23:27): If f(x³-4)+f(4-4x)= x²-2x find d/dx(f(x))
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Complex_Numbers/1205712 (2024-01-20 14:22:41): If f(x³-4)+f(4-4x)= x²-2x finf d/dx(f(x))
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Complex_Numbers/1205711 (2024-01-20 14:21:32): إذا f(x³-4)+f(4-4x)= x²-2x تجد d/dx(f(x))
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Linear-systems/1205688 (2024-01-19 07:37:34): If T: R³→ R³ is If is a linear transformation defined by T(x,y,z)=(x+2y,x−y+z,−2y+z) Write the primary decomposition of R³
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Probability-and-statistics/1205591 (2024-01-11 09:18:42): After selecting a sample containing 27 observations, it is calculated that
∑X=10
∑Y=2
∑X^2=160
∑Y^2=420
1)Construct the equation of the linear regression.
2)Determine the confidence interval for the coefficient 𝛼 with a significance level of 0.02.
3)Test the hypothesis with a probability of 0.95:
H0: 𝛼 ≤ 0,
H1: 𝛼 > 0.
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Probability-and-statistics/1205589 (2024-01-11 09:12:56): At the same distance with the same measuring device, B was measured 8 times. The average measurement result was 202m, with an average square deviation of s=0.7m.
1)Determine the confidence interval for the mathematical expectation of the measurement of distance B with a probability of 0.92.
2)Test the hypothesis: H0: σ^2 ≥ 0.65, H1: σ^2 < 0.65, with a significance level of 0.1.
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Linear_Algebra/1205507 (2024-01-02 01:42:30): If TA is multiplication by a matrix A with three columns, then the kernel of TA is one of four possible geometric objects. What are they? Explain how you reached your conclusion
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test/1205503 (2024-01-01 11:39:34): Express the following as a product of transposition in two ways.
1. [1 2 2 1 3 4 4 3 5 6 6 5 7 8 8 7 ]
2. [1 2 2 1 3 4 4 5 5 6 3 7 7 8 8 6 ]
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test/1205502 (2024-01-01 11:38:44): Express each of the following permutations of [ 1 2 3 4 5 6 7 8 ] as a product of transpositions.
1. [1 2 3 4 3 4 5 6 5 6 8 2 7 8 7 1 ]
2. [1 2 1 3 3 4 8 4 5 6 6 7 7 8 5 2 ]
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Permutations/1205501 (2024-01-01 11:36:44): Express each of the given permutation of [ 1 2 3 4 5 6 7 8 ] as a product of disjoint cycles.
[1 2
3 6
3 4
4 5
5 6
1 7
7 8 8 2 ]
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Probability-and-statistics/1205409 (2023-12-16 10:00:29): Given the joint density function
f(x,y) = {(x(1+3y^2)/4 0
Find a. g(x) b. h(y), and evaluate P(1/4
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Probability-and-statistics/1205407 (2023-12-16 09:57:02): Suppose that X and Y Have the following joint probability distribution
f(x,y) x 2 4
1 0.10 0.15
y 3 0.20 0.30
5 0.10 0.15
a. Find the marginal distribution of X.
b. Find the marginal distribution of Y.
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Evaluation_Word_Problems/1205323 (2023-12-09 06:48:40): Siti has RM450000 in her ASB. She wants to invest in Gading Mutual deposit, Maju
Makmur bar gold, Indah certificate deposit and Selamat Maju bar gold which pay
simple annual interest of 9%, 6%, 10% and 15%, respectively. Moreover, she wants
to combine annual return of 8% and want to have only one-third of investment in
Indah certificate deposit and Selamat Maju bar gold.
a. Write the linear model system equation for the whole investment.
c. Use elimination method to find each of the investment
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Central-limit-theorem/1205257 (2023-12-04 19:58:45): 1. An investigator decided to construct a frequency distribution with five classes. The following
information was available. For fifty observations made on a characteristic under study, the
first two and the last two frequencies were 6,10,10 and 6 respectively. Given the last class
mark is 66 and upper class limit of the fifth class is 72.
a. Calculate mean, Median and mode.
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Matrices-and-determiminant/1205220 (2023-12-02 11:41:15): Determine the order of the following elements.
a) [1 2 3 4 5 2 3 4 5 1]
b) [1 2 3 4 4 3 1 2 ]
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Probability-and-statistics/1205202 (2023-12-01 03:31:46): 1. Considering the following distribution for blood pressure level of male patients in a given hospital
(in mm Hg).
Values (BP) Frequency (# of patients)
140- 150 17
150- 160 29
160- 170 42
170- 180 72
180- 190 84
190- 200 107
200- 210 49
210- 220 34
220- 230 31
230- 240 16
240- 250 12
Calculate:
a) All the quartiles.
b) Find the 8th deciles.
c) Find the 20th percentiles
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Equations/1205173 (2023-11-29 10:56:07): Consider the following system of linear equations
𝑥 + 3𝑦 + 2𝑧 − 𝑤 = −1
−3𝑥 − 7𝑦 + (𝑝 − 6)𝑧 + 2𝑤 = 1
2𝑥 + 𝑝^2𝑧 + 𝑝𝑤 = 𝑞^2
where 𝑝 and 𝑞 are real numbers.
Using Gaussian elimination, determine all possible values of 𝑝 and 𝑞 such that the system has infinitely many solutions with two free variables and solve the systems
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Equations/1205169 (2023-11-29 10:39:04): Consider the following system of linear equations:
𝑥 + 3𝑦 + 2𝑧 − 𝑤 = −1
−3𝑥 − 7𝑦 + (𝑝 − 6)𝑧 + 2𝑤 = 1
2𝑥 + 𝑝^2𝑧 + 𝑝𝑤 = 𝑞^2
where 𝑝 and 𝑞 are real numbers.
Using Gaussian elimination, determine all possible values of 𝑝 and 𝑞 such that the system has infinitely many solutions with two free variables and solve the system.
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Permutations/1205136 (2023-11-27 13:49:45): Student A was tasked to program an algorithm for a number generator. The generator will be used by A Soda Company for their bottlecaps.
Soda Company will be holding a bottlecap lottery where 5 select bottlecaps will be winning combinations. There would be three characters printed on the bottlecaps with each character having the chance to be repeated. Those that are not winning codes are duplicated 10 times.
If Student B, was to join, how many bottles of Soda will he need to buy to have a 1% chance at winning.
And if Student C would join too, what is the chance that 24 bottlecaps have at winning?
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Permutations/1205135 (2023-11-27 13:46:20): Student A was tasked to program an algorithm for a number generator. The generator will be used by Soda Co. for their bottlecaps.
Soda Co. will be holding a bottlecap lottery where 5 select bottlecaps will be winning combinations. There would be three characters printed on the bottlecaps with each character having the chance to be repeated. Those that are not winning codes are duplicated 10 times.
If Student B was to join, how many bottles of Soda will he need to buy to have a 1% chance at winning.
And if Student C would join too, what is the chance that having 24 bottlecaps have a chance at winning?
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Probability-and-statistics/1205113 (2023-11-25 22:41:16): In a soccer league consisting of 𝑛 soccer teams, each soccer team plays against every other soccer team twice. against every other soccer team 2 times. Each match awards a certain number of points for a soccer team based on the result that the soccer team gets in the match. match. A win, a draw, and a loss give a soccer team 𝑎, 𝑏, and 𝑐 points respectively in each match; where 𝑎 + 𝑐 > 2𝑏 and 𝑏 > 𝑐. The final ranking of the soccer league will be based on the points earned by the soccer teams after competing against by the soccer teams after competing against each of the other soccer teams twice. The soccer team that earns more points will be ranked higher than the soccer team that earns less points.
than the soccer team with fewer points. If 2 or more football teams achieve the same number of points, then the ranking among them will be randomly drawn. In
the soccer league, a soccer team wishes to be ranked at least𝑘th or higher in the final ranking. or higher in the final ranking of the soccer league. State the minimum points that the soccer team must get in 𝑎, 𝑏, 𝑐, 𝑛, and 𝑘
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Probability-and-statistics/1205112 (2023-11-25 22:34:45): Suppose 𝑋1, 𝑋2, . . . is a discrete time Markov chain with the set of state spaces state space 𝑆 = {1, 2, 3, 4, 5, 6} and the transition probability matrix as follows:
𝑃 =
[
0 0 0.5 0.5 0 0
0 0 1 0 0 0
0 0 0 0 0.5 0.5
0 0 0 0 1 0
0.5 0.5 0 0 0 0
1 0 0 0 0 0
]
Find:
(a) 𝑃(𝑋3000000 = 2 | 𝑋0 = 1)
(b) 𝑃(𝑋3000001 = 2 | 𝑋0 = 1)
(c) 𝑃(𝑋3000002 = 2 | 𝑋0 = 1)
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Probability-and-statistics/1205111 (2023-11-25 22:32:13): Cars entering a highway section have an increasing speed during a certain time interval and follow a nonhomogeneous Poisson process with a rate of
𝜆(𝑡) = 18𝑡 per hour. The duration or time spent by cars on the highway section is a uniformly distributed random variable in the interval [2, 4] hours. Assume that there is no interaction between cars and the random times of cars on the toll road are independent. Suppose 𝐴(𝑡) is the number of cars entering the toll road section during [0, 𝑡] and suppose 𝑋(𝑡) is the number of cars in the toll road section at time 𝑡.
Determine
(a) 𝑃(𝐴(2) = 40 | 𝐴(1) = 20)
(b) 𝐸[𝑋(10)]
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Matrices-and-determiminant/1205106 (2023-11-25 17:05:46): Let A and B be the following matrices:
A rotates vectors clockwise by a right angle. B projects vectors onto a line with direction (1; 4).
I don't know how to format matrices on here, so I will write the top row (horizontal) and the bottom row. This is a 2 x 2 matrix.
Calculate the matrix AB[-4 1][1 4].
Sorry if the matrices are unclear. In latex, you are calculating $\[\mathbf{A}\mathbf{B} \begin{pmatrix} -4 & 1 \\ 1 & 4 \end{pmatrix}.\]$
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Permutations/1205063 (2023-11-22 03:36:20): You were tasked to program an algorithm for a number generator. The generator will be used by a soda company for their bottlecaps. The soda company will be holding a bottlecap lottery where 5 select bottlecaps will be winning combinations. There would be three characters printed on the bottlecaps with each character having the chance to be repeated. If a second person was to join, how many bottles of Pepsi will the 2nd person need to buy to have a 1% chance at winning.
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Travel_Word_Problems/1204892 (2023-11-13 01:52:35): A cat walks in a straight line, which we shall call the x-axis, with the positive direction to the right. As an observant physicist, you make measurements of this cat's motion and construct a graph of the feline's velocity as a function of time (Fig. E2.26). (link for the Fig. E2.26: https://i.postimg.cc/fRgY00DK/Figure-E2-26.png )
(a) Find the cat's velocity at t = 4.0s and at t = 7.0s.
(b) What is the cat's acceleration at t = 3.0s? At t = 6.0s? At t = 7.0s?
(c) What distance does the cat move during the first 4.5s? From t = 0 to t = 7.0s?
(d) Assuming that the cat started at the origin, sketch clear graphs of the cat's acceleration and position as functions of time.
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Travel_Word_Problems/1204891 (2023-11-13 01:18:28): Consider the motion described by the vx-t graph of Fig. E2. 26. (see this link--> https://i.postimg.cc/SsGt7snK/Fig-E2-26.png )
(a) Calculate the area under the graph between t=0 and t=6.0s.
(b) For the time interval t=0 to t=6.0s, what is the magnitude of the average velocity of the cat?
(c) Use constant-acceleration equations to calculate the distance the cat travels in this time interval. How does your result compare to the area you calculated in part (a)?
problem from Young and Freedman. University Physics with Modern Physics Fifteenth Edition.
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Travel_Word_Problems/1204877 (2023-11-12 12:44:42): The acceleration of a bus is given by ax(t) = at, where a = 1.2m/s^3.
(a) If the bus's velocity at time t = 1.0s is 5.0 m/s, what is its velocity at time t = 20 s?
(b) If the bus's position at time t = 1.0 s is 6.0 m, what is its position at time t = 2.0 s?
(c) Sketch ay-t, vy-t and x-t graphs for the motion.
problem from Young and Freedman. University Physics with Modern Physics. Fifteenth Edition.
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Complex_Numbers/1204865 (2023-11-12 07:57:29): if : f '(g (x)) = g '(x), f ''(x) \[Times] f '(x) = f (x), g '(3) = 2 g ''(3) = 2} then (d ^5 g)/(dx ^5 when x=3 is ... (9 , 10 ,18 , 24)
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Complex_Numbers/1204864 (2023-11-12 07:21:03): if : f '(g (x)) = g '(x), f ''(x) \[Times] f '(x) = f (x), g '(3) = 2 g ''(3) = 2} then (d ^5 g)/(dx ^5)| = ... (9 , 10 ,18 , 24)
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Probability-and-statistics/1204805 (2023-11-09 14:14:04): The average BMI (body mass index) of college students is normally distributed with a mean of 25, standard deviation of 5. How many students BMI is between 22 and 29? How many students have a BMI of more than 29? How many students have a BMI of less than 22? What level of BMI would put you in the bottom 5% of the weight distribution? Top 5%?
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Probability-and-statistics/1204803 (2023-11-09 14:08:06): During my office hours (12pm to 6pm), an average of 2 students per hour comes in for help. Assuming that the probability of a student coming in is uniform throughout my office hours, what are the odds that on a particular day I would have 6 students come in for help? What is the mean number of students that will come see me on a particular day? Variance? Standard deviation?
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testmodule/1204472 (2023-10-23 20:10:57): Two special training programs in outdoor survival are available for army recruits. One
lasts one week and the other lasts two weeks. The officer wishes to test the effectiveness
of the program and see whether there are any gender differences. Six subjects are
randomly assigned to each of the program according to gender. After completing the
program, each is given a written test on his/hers knowledge of survival skills. The test
consists of 100 questions. The scores of the groups are shown here.
Duration
Gender One Week Two Weeks
Female 86, 92, 87, 88, 78, 95 78, 62, 56, 54, 65, 63
Male 52, 67, 53, 42, 68, 71 85, 94, 82, 84, 78, 91
Use the values listed in the table below to answer the question.
Source SS
Gender 57.042
Duration 7.042
Interaction 3978.375
Error 1365.5
Total 5407.959
a) Is there a difference between the means of the test scores for the two different
durations. Use α = 0.05.
b) Is there a difference in the means of the test scores between the gender. Use α = 0.1.
c) Is there an interaction effect between the gender of the individual and the duration
of the training on the test scores. Use α = 0.01
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testmodule/1204471 (2023-10-23 20:09:55): The yields of wheat (in kilogram per hectare) were compared for five different varieties,
A, B, C, D, and E, at six different locations. Each variety was randomly assigned a
plot at each location. The results of the experiment are shown in the table:
Location
Variety 1 2 3 4 5 6
A 35.3 31.0 32.7 36.8 37.2 33.1
B 30.7 32.2 31.4 31.7 35.0 32.7
C 38.2 33.4 33.6 37.1 37.3 38.2
D 34.9 36.1 35.2 38.3 40.2 36.0
E 32.4 28.9 29.2 30.7 33.9 32.1
Use the partially completed ANOVA table to answer the following questions:
Table 1: ANOVA Table
Source df SS MS F
Treatments 142.67
Blocks 68.1417
Error
Total 249.1417
a) Do the data present sufficient evidence to indicate a difference in the mean yields
of wheat for the five different varieties? Test using α = 0.05.
b) Do the data present sufficient evidence to indicate difference in the mean yields of
wheat for the six different locations? Test using α = 0.01.
c) Use Tukey’s method for paired comparisons to determine which of the treatment
means differ significantly from the others. Test using α = 0.05.
d) Find a 95% confidence interval for the difference in means for treatments B and D.
e) Find a 98% confidence interval for the difference in means for blocks 1 and 3.
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Probability-and-statistics/1204410 (2023-10-20 20:28:59): The expected number of defective parts produced on an assembly line per shift is 50 with a standard deviation of 8. Use Chebyshev's inequality to find the minimum probability that the number of defective parts on a particular shift will be between 22 and 78. (Round your answer to four decimal places.)
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Matrices-and-determiminant/1204386 (2023-10-19 23:48:26): Let a ∈ R^n be a vector. Then {a} is linearly independent if and only if a does not equal 0.
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Trigonometry-basics/1204330 (2023-10-17 22:20:02): Find the sum
𝑆 = cos(𝑥 + 𝜃) + cos(2𝑥 + 3𝜃) + cos(3𝑥 + 5𝜃) + cos(4𝑥 + 7𝜃) + ⋯ + cos(40𝑥 + 79𝜃),
and express your answer as a product and quotient of trigonometric functions.
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Probability-and-statistics/1204322 (2023-10-17 18:37:24): The expected number of defective parts produced on an assembly line per shift is 50 with a standard deviation of 8. Use Chebyshev's inequality to find the minimum probability that the number of defective parts on a particular shift will be between 22 and 78. (Round your answer to four decimal places.)
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Probability-and-statistics/1204266 (2023-10-15 10:06:44): Once a baby is born, an option becomes available to harvest the stem cells of the child from the umbilical cord. This is done at the hospital, in the labour ward. The specimen must be cooled very quickly and maintained at the same temperature for extended periods (often many years). Three competing refrigeration units are tested against one another by the claim that they are able to reduce the temperature of the specimen, in the hospital, to the required level in a minimum amount of time. The refrigeration units are tested at 27 randomly allocated labour wards around the Western Cape. The rate at which the desired temperature is reached (in seconds) is below.
Refrigeration Unit : Temperature rate (in seconds)
Unit 1 : 82; 61; 63; 91; 88; 71; 59; 65; 58; 49
Unit 2 : 67; 58; 72; 71; 54; 79; 44; 60; 77
Unit 3 : 91; 112; 84; 81; 76; 54; 82; 64
Calculate at a 10% level of significance whether there is a significant difference between the mean time until the correct temperature is reached in the three refrigeration units.
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Probability-and-statistics/1204179 (2023-10-11 12:02:45): Given a random variable X, with standard deviation σX, and a random variable Y = a + bX, show
that if b < 0, the correlation coefficient ρXY = −1, and
if b > 0, ρXY = 1
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Probability-and-statistics/1204126 (2023-10-09 08:25:47): Let X and Y be jointly normal random variables with parameters µ_X = 1, (σ_X)^2= 1, µ_Y = 0, (σ_Y)^2= 4, and ρ = 1/2.
(a) Find P(2X + Y < 3).
(b) Find P(Y > 1|X = 2).
(c) Find conditional expectation of Y given X = 2.
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Mixture_Word_Problems/1204112 (2023-10-08 08:24:01): Word Problem Create a mch Find the matart vector in each problem and direction
1. An airplane is flying 340 km/hr at 12° North of Pan. The wind is blowing 40 km at 34° South of East What is the plane actual velocity?
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Complex_Numbers/1204107 (2023-10-08 00:22:37): We may define a complex conjugation operator K such that Kz =z^ * . Show that K is not a linear operator
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Describing-distributions-with-numbers/1204046 (2023-10-04 07:33:13): The amount of caffeine in a sample of 250ml servings of brewed coffee is summarized in the table below:
Caffeine (mg) Number of cups
60 < 80 : 1
80 < 100 : 12
100 < 120 : 25
120 < 140 : 10
140 < 160 : 2
2.1 Calculate the average caffeine content of the 250ml cup
2.2 Calculate the modal caffeine content of the 250ml cup.
2.3 Calculate the median caffeine content of the 250ml cup.
2.4 Calculate the standard deviation of the content of the 250ml cup
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Probability-and-statistics/1203976 (2023-09-29 19:16:40): Three assembly lines are used to produce a certain component for an airliner. To examine the production rate, a random sample of six hourly periods is chosen for each assembly line and the number of components produced during these periods for each line is recorded. The output from a statistical software package is:
Summary
Groups Sample Size Sum Average Variance
Line A 6 250 41.66667 0.266667
Line B 6 260 43.33333 0.666667
Line C 6 249 41.5 0.7
ANOVA
Source of Variation SS df MS F p-value
Between Groups 12.33333 2 6.166667 11.32653 0.001005
Within Groups 8.166667 15 0.544444
Total 20.5 17
Compute 99% confidence intervals that estimate the difference between each pair of means. (Negative amount should be indicated by a minus sign. Round your answers to 2 decimal places.) Which pairs of means are statistically different?
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Probability-and-statistics/1203807 (2023-09-22 05:06:48): A function f(x) has the following form:
f(x)=kx^-(k+1) 1
and zero otherwise.
(a)For what values of k is f(x) a pdf?
(b)Find the CDF based on (a).
(c)For what values of k does E(X) exist?
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