Question

In: Statistics and Probability

Airlines sometimes overbook fights. Suppose that for a plane with 50 seats, 53 passengers have tickets....

Airlines sometimes overbook fights. Suppose that for a plane with 50 seats, 53 passengers have tickets. Define the random variable Y as the number of ticketed passengers who actually show up for the fight. The probability mass function of Y appears in the accompanying table.

Y 48 49 50 51 52 53 P(Y=y) 0.28 ? 0.25 0.06 0.05 0.05

a. Given the missing value P(Y=49).

b. What is the probability that the fight will accommodate all ticketed passengers who show up?

c. If you are the first person on the standby list (which means you will be the first one to get on the plane if there are any seats available after all ticketed passengers have been accommodated), what is the probability that you will be able to take the flight?

d. Find E(Y) and E(Y^2).

e. Find V(Y).

Solutions

Expert Solution

Following is the probability mass function of Y,

a) Since the total probability must some upto 1, we have,
​​​​​​  
And so the probability mass function of Y is given as,

orchestra answered 1 year ago
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