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29 August, 00:37

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

+2
Answers (1)
  1. 29 August, 01:28
    0
    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

    Step-by-step explanation:

    Answer: 23.18 (nearest hundredth)
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