Mathematics, 23.04.2020 20:59 lksocossiodks8855
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 0 1 2 3 4 5
P(X = x) = f(x) 0.1 0.2 0.2 0.3 0.1 0.1
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 (remember the shuttle can only hold 4 people).
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?
d. Compute the expectation and variance of X.
e. What is the expected value of 200X − 100?
f. What is expected value of X2 ?
Answers: 2
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Say there is a shuttle that has 4 seats (it can carry only 4 passengers at most). The shuttle driver...
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