Consider the probability distribution below. The variance of x equals
A) 9.
B) 23.
C) 81.
D) 610.

Question

Consider the probability distribution below.  ​ The variance of x equals
A) 9. 
B) 23. 
C) 81. 
D) 610.

Quizplus · Accepted Answer

To calculate variance, we need to first find the mean of the distribution. 
Mean = (2(0.2) + 3(0.3) + 4(0.1) + 5(0.2) + 6(0.1) + 7(0.1)) = 4.2 
Then, we can use the formula for variance: 
Variance = E[(x - E[x])^2] = (0.2(2-4.2)^2 + 0.3(3-4.2)^2 + 0.1(4-4.2)^2 + 0.2(5-4.2)^2 + 0.1(6-4.2)^2 + 0.1(7-4.2)^2) 
= 0.84 + 0.246 + 0.004 + 0.084 + 0.268 + 0.268 
= 1.71

Thus, the variance of x is 1.71, which is closest to choice C (81). The other answer choices are significantly larger than the actual variance.

Consider the Probability Distribution Below