Question 1047561: Can someone check my answers to these questions to tell me if I did the correctly. If not, please show me how.
Answer questions 1-5 based on the probability distribution table below:
x 0 1 2 3
p(x) .1 .2 .3 .4
1. List the values that x may assume.
{(0, 0.1, 0.2, 0.3, 0.4, 0.2, 0.4, 0.6, 0.8, 0.3, 0.6, 0.9, 1.2)}
2. What value of x will occur most often?
0.2, 0.3, 0.4, 0.6
3. What is the probability that x will be greater than zero?
.3 + .4 = .7
.7/2 = .35
4. Calculate the expected value for the data set.
EX = 0 * .1 + 1 * .2 + 2 * .3 + 3 * .4
0 * 1 = 0
0 + 1 * .2 = 0.2
0.2 + 2 *.3 = 0.8
0.8 + 3 *.4 = 2
The expected value for the data set is 2.
5. Calculate the variance for the data set.
V = (X - E(X))^2
V = (0 - 2)^2 * .1 + (1 - 2)^2 * .2 + (2 - 2)^2 * .3 + (3 - 2)^2 * .4
V = (-2)^2 * (.1) + (-1)^2 * (.2) + (0)^2 * (.3) + (1)^2 * (.4)
V = (4) * (.1) + (1) * (.2) + (0) * (.3) + (1) * (.4)
V = 0.4 + 0.2 + 0 + 0.4
V = 1
A discrete random variable x can assume five possible values: 5, 10, 15, 20, and 25. Answer questions 4-8 based on the probability distribution shown here:
x 5 10 15 20 25
p(x) .15 .10 ? .25 .25
6. What is the probability that x = 15?
.15 + .10 + .25 + .25 = 0.75
0.75/5
0.15
7. What is the probability of x ≥20?
.25 + .25 = .5
8. If we constructed a histogram would the data be skewed or symmetric?
If we constructed a histogram, the data be skewed.
9. Calculate the expected value (mean) given the probability distribution above.
EV = 5 * .15 + 10 * .10 + 15 *.15 + 20 * .25 + 25 * .25
EV = .75 + 1 + 2.25 + 5 + 6.25
EV = 15.25
10. Calculate the variance given the probability distribution above.
v =5 * .15 + 10 * .10 + 15 * .15 + 20 * .25 + 25 * .25
v = (5 - 15.25)^2 * .15 + (10 – 15.25)^2* .10 + (15 – 15.25 * .15 + (20 – 15.25 * .25 + (25 – 15.25)^2 * .25
v = (-10.25)^2 *.15 + (-5.25)^2* .10 + (-.25)^2 * .15 + (4.75)^2 * .25 + (9.75)^2 * .25
v = 105.0625 *.15 + 27.5625 * .10 + 0.0625 * .15 + 22.5625 * .25 + 95.0625 * .25
v = 15.759375 + 2.75625 + 0.009375 + 5.640625 + 23.765625
v = 18.515625 + 0.009375 + 29.40625
v = 18.525 + 29.40625
v = 47.93125
v = 47.93
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! 1. X may assume 0,1,2,3
2. 3 will occur most often, because the probability is greatest.
3. The probability x will be greater than 0 is 0.9, because probability of 0 is 0.1 and that is the only probability excluded.
4. E(x)=x*p(x)=
0*0.1+1*0.2+2*0.3+3*0.4=0+0.2+0.6+1.2=2.
E(x)=2
5.V(x)=0.4+0.2+0+0.4=1.0, again as you had.
6. 0.75 is the sum of the other probabilities. The probability of x's being 15 is 0.25.
7. Correct as you had it.
8.Slightly skewed. It isn't symmetric, so skewed it must be.
9.Expected value is 16.75 The value of 15 has probability 0.25, so it contributes 3.75 to the sum.
10. (5-16.75)^2*0.15=20.709375
(10-16.75)^2*0.10=4.55625
(15-16.75)^2*0.25=0.765625
(20-16.75)^2*0.25=2.640625
(25-16.75)^2*0.25=17.015625
Sum is 45.6875
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