Solution Found!
Let X equal the number of people selected at random that you must ask in order to find
Chapter 2, Problem 2.3-12(choose chapter or problem)
Let X equal the number of people selected at random that you must ask in order to find someone with the same birthday as yours. Assume that each day of the year is equally likely, and ignore February 29.
(a) What is the pmf of X?
(b) Give the values of the mean, variance, and standard deviation of X.
(c) Find P(X > 400) and P(X < 300).
Questions & Answers
QUESTION:
Let X equal the number of people selected at random that you must ask in order to find someone with the same birthday as yours. Assume that each day of the year is equally likely, and ignore February 29.
(a) What is the pmf of X?
(b) Give the values of the mean, variance, and standard deviation of X.
(c) Find P(X > 400) and P(X < 300).
ANSWER:Step 1 of 4
(a) Each day is equally likely. Since there are 365 days in a year (ignore February 29), we have 1 chance in 365 that somebody else's birthday is on your birthday.
We are interested in the first success among independent trials with a constant probability of success, which follows a geometric distribution.
Definition geometric probability:
In this case:
