discrete random variable statistics

Question

Consider the following distribution for a discrete random variable

X      -1    0    1   2     3

P(X=x)0.2  0.1  0.4  0.25  0.05

(a) Find the probability P(X >1)

(b) Find the conditional probability P(X >1|X≥0)

(c) Calculate the expected valueE[X].

(d) Find the variance by calculating E[(X−E[X])^2] showing details.

Answer 1

a .3

add the last two probabilities: .05 + .25

b .3/.8 = .325

.3/(1-.2) = 3/8

c .85

take the weighted average, each x weighted by it's probability

-1(2) + 0(.1) + 1(.4) + 2(.25) + 3(.05)

= -.2 +.4 + .5 + .15 = .85