Question

The following table shows the probability distribution for a discrete random

variable.
Х
11
14
16
19
21
23
24
29
P(X) 0.07 0.21
0.17 0.25 0.05 0.04 0.13 0.08
What is the mean of this discrete random variable? (That is, what is E(X), the
expected value of X?)
A. 19
B. 19.625
C. 20
D. 18.59

Answer 1

Answer: 18.59

Explanation:

A P E X

Answer 2

Because the random variable X is discrete, the variance of X is defined as

var(X) =

where

p = values of probability as given in the table.

μ = 18.59

Calculate the array (x - μ).

x-μ = [-7.59 -4.59 -2.59 0.41 2.41 4.41 5.41 10.41]

Calculate the array (x-μ)².

(x- μ)² = [57.6081 21.0681 6.7081 0.1681 5.8081 19.4481 29.2681 108.3681]

Calculate the array p*(x-μ)².

p*(x- μ)² = [4.0326 4.4342 1.1404 0.042 0.2904 0.7779 3.8049 8.6694]

Calculate the variance of X.

var(X) = 23.182

Explanation:

Answer: 23.18 (nearest hundredth)