Let X equal the number of people selected at random that you

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 value of the mean of X.

(c) Find P(X > 400) and P(X < 300).

Solution

X: number of people selected at random that you must ask in order to find someone with the same birthday as yours.

now ignoring 29th february there are 365 days in a year.

so the probability that the person\'s birthday will be as same as yours is 1/365

here the assumption is that each day of the year is equally likely.

a) so pmf of X is

f(x)=(1-1/365)^x-1*(1/365)        x=1,2,3,............................

     = 0              otherwise

b)the mean value of X is E[X]=(1/365)^-1=365 [answer]

c)P[X>400]=1-P[X<=400]=1-0.666260=0.33374 [answer]

P[X<300]=P[X<=299]=0.559701 [answer]