Question

7.19 We are given the following probability distribution. x P(x) b. c. d. 0 1 2 3 .1 .4 .3 .2 a. Calculate the mean, variance, and standard deviation.

Answer 1

Mean = 1.6

Variance = 0.84

Standard deviation = 0.916

Explanation:

We are given the following probability distribution below;

X P(X)
`X * P(X)`
`X^(2) * P(X)`

0 0.1 0 0

1 0.4 0.4 0.4

2 0.3 0.6 1.2

3 0.2 0.6 1.8

Total 1.6 3.4

Now, the mean of the probability distribution is given by;

Mean, E(X) =
`\sum X * P(X)` = 1.6

Also, the variance of the probability distribution is given by;

Variance, V(X) =
`\sum X^(2) * P(X) - (\sum X * P(X))^(2)`

=
`3.4 - (1.6)^(2)`

= 3.4 - 2.56 = 0.84

And the standard deviation of the probability distribution is given by;

Standard deviation, S.D. (X) =
`√(Variance)`

=
`√(0.84)` = 0.916.