Question

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).

Answer 1

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.

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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"

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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".

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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