On hot sunny summer days Jane rents inner tubes by the river

On hot, sunny, summer days, Jane rents inner tubes by the river that runs through her town. Based on her past experience, she has assigned the following probability distribution to the number of tubes she will rent on a randomly selected day. x 25 50 75 100 Total P(x) .20 .40 .30 .10 1.00 Find the probability expressions a. P(X = 75) b. P(X 75) c. P(X > 50) d. P(X < 100) Which of the probability expressions in parts (a)–(d) is a value of the CDF? Part (a) Part (b) Part (c) Part (d)

Solution

a. P(X=75) = 0.3

b. P(X less than or equal to 75)= P(X=25)+P(X=50)+P(X=75)= .2+.4+.3= 0.9

c. P(X greater than 50)= P(X=75)+P(X=100) = .3+.1= 0.4

d. P(X less than 100)= P(X=25)+P(X=50)+P(X=75)= .2+.4+.3= 0.9

Part b is cdf value at 75