Question

Given tGiven the following probability distribution, find P (X = 3).

X 1 2 3 4 5
P(X) 0.4 0.1 0.15 0.2
(1 point)

2. The number of cars an American family owns follows the distribution below:

Number of Cars0 1 2 3 4 5
Probability 0.090.36 0.350.13 0.050.02


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). (5 points)

3. A study of social mobility in America examined the social class attained by the sons of lower class fathers. Social classes were numbered from 1 to 5 with 1 representing the lower class and 5 the higher class. Consider the random variable X to the class of a randomly chosen son. The study found the following distribution:

Son's Class1 2 3 4 5
Probability0.48 0.38 0.08 0.05 0.01

a) What percent of the sons reached the highest class?
b) Check that this distribution meets the requirements of a discrete probability distribution.
c) What is P(X < 2)?
d) What is P(X = 2)?
e) Write the event: a son of a lower-class father attains one of the highest two social classes in terms of X. (6 points)

Answer 1

1.) P(X = 3) = 1 - (0.4 + 0.1 + 0.15 + 0.2) = 1 - 0.85 = 0.15

2a.) To verify that the probability is legimate, we sum it and see if the sum is 1. 0.09 + 0.36 + 0.35 + 0.13 + 0.05 + 0.02 = 1
Since the sum of the probabilities is 1, the probability is a legitimate probability distribution.
b.) P(x > 2) is the probability that the number of cars an American family owns is greater than 2.
c.) P(x = 2) is the probability that the number of cars an American family owns is 2.
d.) P(x > 2) => P(x = 3) + P(x = 4) + P(x = 5) = 0.13 + 0.05 + 0.02 = 0.2

3a.) The percent of the sons that reached the highest class is 0.01 x 100% = 1%
b.) 0.48 + 0.38 + 0.08 + 0.05 + 0.01 = 1
Since the sum of the probabilities is 1, the distribution meets the requirements of a discrete probability distribution.
c.) P(x < 2) = P(x = 1) = 0.48
d.) P(x = 2) = 0.38