the number of people with tickets that show up to ride the shuttle. The probability mass function (pmf) of X is as follows: IC

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a. Verify that f(x) is a valid probability mass function.

b. Find the probability that the shuttle will be able to accommodate all ticketed people that show up.

c. Say you are the 1st person on the wait list to get on the shuttle (that is to say if less than 4 people with tickets show up, you get a seat). What is the probability that you will be able to board the shuttle?

1. Say there is a shuttle that has 4 seats (it can carry only 4 passengers at most). The shuttle
driver has sold 5 tickets to ride the shuttle (to 5 people). Define X to be the random variable of
the number of people with tickets that show up to ride the shuttle. The probability mass function
(pmf) of X is as follows:
X
P(X = X =
XOL
f(x)
0
2
0.1 0.2 0.2
3 4 5
0.3
0.1 0.1
Transcribed Image Text:1. Say there is a shuttle that has 4 seats (it can carry only 4 passengers at most). The shuttle driver has sold 5 tickets to ride the shuttle (to 5 people). Define X to be the random variable of the number of people with tickets that show up to ride the shuttle. The probability mass function (pmf) of X is as follows: X P(X = X = XOL f(x) 0 2 0.1 0.2 0.2 3 4 5 0.3 0.1 0.1
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