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:
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)
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
