Consider the probability distribution shown below.

Question

Consider the probability distribution shown below.

x	0	1	2
P(x)	0.65	0.20	0.15

Compute the expected value of the distribution. (Enter a number.)

Compute the standard deviation of the distribution. (Enter a number. Round your answer to four decimal places.)

Answer 1

E(x) = sum(x*p(x)) over all x= .65 * 0 + .2 * 1 + .15 * 2 = 0.50

std.dev(x) = sqrt(variance(x)) = sqrt(E[X^2 ] - (E[X])^2).

E(x^2) = .65 * 0^2 + .2 * 1^2 + .15 * 2^2 = .2 + .6 = .8

(E(x))^2 = .50^2 = .25

so std.dev(x) = sqrt(.8 - .25) = sqrt(.55) ~ 0.7416198