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)