Question

The probability function of a random variable X is given by
p(x) = `{{:(1/4",",  "for"  x = - 2),(1/4",",  "for"  x = 0),(1/2",",  "for"  x = 10),(0",",  "elsewhere"):}`
Evaluate the following probabilities
P(|X| ≤ 2)

Answer 1

X	– 2	0	10
P(X = x)	`1/4`	`1/4`	`1/2`

P(|x| ≤ 2) = P(– 2 ≤ X ≤ 2)

= P(X = – 2) + P(X = 0) 

= `1/4 + 1/4`

= `2/4`

= `1/2`