(d*) What is the expected number of Columbia affiliates in your sample? What is the variance of this number? (e*) Suppose you keep asking people until you find 10 that are not Columbia affiliates, and then you go home. How many people do you have to ask on average until you can go home?

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Please answer D and E only

Exercise 8
Suppose that 70% of the people coming out of a particular exit of 116th Street Station are Columbia
University affiliates. You wait at the exit and ask 10 people whether they are Columbia affiliates
or not.
(a*) What is the probability that the third, the fifth and the tenth person are Columbia affiliates?
(b*) What is the probability that the third, the fifth and the tenth person are Columbia affiliates
and all others are not?
(c*) What is the probability that you find exactly three Columbia affiliates?
(d*) What is the expected number of Columbia affiliates in your sample? What is the variance of
this number?
(e*) Suppose you keep asking people until you find 10 that are not Columbia affiliates, and then
you go home. How many people do you have to ask on average until you can go home?
Transcribed Image Text:Exercise 8 Suppose that 70% of the people coming out of a particular exit of 116th Street Station are Columbia University affiliates. You wait at the exit and ask 10 people whether they are Columbia affiliates or not. (a*) What is the probability that the third, the fifth and the tenth person are Columbia affiliates? (b*) What is the probability that the third, the fifth and the tenth person are Columbia affiliates and all others are not? (c*) What is the probability that you find exactly three Columbia affiliates? (d*) What is the expected number of Columbia affiliates in your sample? What is the variance of this number? (e*) Suppose you keep asking people until you find 10 that are not Columbia affiliates, and then you go home. How many people do you have to ask on average until you can go home?
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