The number of cars an american family owns follows the distribution below: number of cars 0 1 2 3 4 5 probability 0.09 0.36 0.35 0.13 0.05 0.02 a) verify that this is a legitimate probability distribution. b) interpret (in words) the notation p(x > 2). c) interpret (in words) the notation p(x = 2). d) find p(x > 2).

Part A)

Add up the probability values to get:

0.09+0.36+0.35+0.13+0.05+0.02 = 1

since we get 1 as a result, this confirms we have a legitimate probability distribution. 



Part B)

The notation P(X > 2) translates to "the probability that X is larger than 2". In this problem's context, it means "the probability of choosing a family that owns more than 2 cars"



Part C)

P(X = 2) means "the probability that X is equal to 2"

Specifically for this problem it means "the probability of picking a family with exactly 2 cars". 



Part D)

Let
A = probability that the family owns exactly 0 cars = 0.09
B = probability that the family owns exactly 1 cars = 0.36
C = probability that the family owns exactly 2 cars = 0.35
D = probability that the family owns exactly 3 cars = 0.13
E = probability that the family owns exactly 4 cars = 0.05
F = probability that the family owns exactly 5 cars = 0.02

Add up the probabilities D, E, and F to compute P(X > 2)

P(X > 2) = probability that the family owns more than 2 cars
P(X > 2) = D + E + F
P(X > 2) = 0.13+0.05+0.02
P(X > 2) = 0.2