SOLUTION: The probability of x is given below
X P(x)
2 .10
4 .20
6 .30
8 .40
Answer the following questions
a) What is the probability that x is less than or equal to 4?
b) Wh
Question 1159943: The probability of x is given below
X P(x)
2 .10
4 .20
6 .30
8 .40
Answer the following questions
a) What is the probability that x is less than or equal to 4?
b) What is the probability that x is greater than or equal to 2?
c) Calculate the expected value
d) Calculate the variance
e) Calculate the standard deviation
The answer is 0.3 since we add the P(x) values when x is 4 or smaller, so when x = 2 or x = 4.
0.10+0.20 = 0.30 = 0.3
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Part b)
"x is greater than or equal to 2" is basically saying "every x value mentioned in the table" because x = 2 is the smallest item listed.
Add up all the P(x) values. You should get 1 as the result. With any probability distribution, all the P(x) values must add to 1 to represent 100%.
Answer = 1
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Part c)
Make a column of the product of the X and P(X) values
X
P(X)
X*P(X)
2
0.1
0.2
4
0.2
0.8
6
0.3
1.8
8
0.4
3.2
Then add up the values in that new third column: 0.2+0.8+1.8+3.2 = 6
Expected value = 6
The expected value is another term for the mean.
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Part d)
Make yet another column. This time we'll represent the X^2*P(X) values
X
P(X)
X*P(X)
X^2*P(X)
2
0.1
0.2
0.4
4
0.2
0.8
3.2
6
0.3
1.8
10.8
8
0.4
3.2
25.6
Those new values add to: 0.4+3.2+10.8+25.6 = 40
Then we subtract off the square of the mean, or expected value, we got back in part c
40 - (mean)^2 = 40 - 6^2 = 40 - 36 = 4
The variance is 4
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Part e)
Apply the square root to the variance to get the standard deviation:
standard deviation = sqrt(variance)
standard deviation = sqrt(4)
standard deviation = 2