Mathematics, 06.08.2019 03:30, dion27

The random variable x has the following probability distribution: x f(x) 0 .25 1 .20 2 .15 3 .30 4 .10 a. is this probability distribution valid? explain and list the requirements for a valid probability distribution. b. calculate the expected value of x. c. calculate the variance of x. d. calculate the standard deviation of x.

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answered: renee9913

Answer and Explanation:

Given : The random variable x has the following probability distribution.

To find :

a. Is this probability distribution valid? Explain and list the requirements for a valid probability distribution.

b. Calculate the expected value of x.

c. Calculate the variance of x.

d. Calculate the standard deviation of x.

Solution :

First we create the table as per requirements,

x P(x) xP(x) x² x²P(x)

0 0.25 0 0 0

1 0.20 0.20 1 0.20

2 0.15 0.3 4 0.6

3 0.30 0.9 9 2.7

4 0.10 0.4 16 1.6

∑P(x)=1 ∑xP(x)=1.8 ∑x²P(x)=5.1

a) To determine that table shows a probability distribution we add up all five probabilities if the sum is 1 then it is a valid distribution.

$\sum P(X)=0.25+0.20+0.15+0.30+0.10$

$\sum P(X)=1$

Yes it is a probability distribution.

b) The expected value of x is defined as

$E(x)=\sum xP(x)=1.8$

c) The variance of x is defined as

$V=\sum x^2P(x)-(\sum xP(x))^2\\V=5.1-(1.8)^2\\V=5.1-3.24\\V=1.86$

d) The standard deviation of x is defined as

$\sigma=\sqrt{V}$

$\sigma=\sqrt{1.86}$

$\sigma=1.136$

answered: Guest

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step-by-step explanation:

answered: Guest

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