Question

Suppose that the class has 36 students. Assume that the birthday of each student

is equally likely to be one of the 365 days of the year, independent of the other student.

(5 points) Let X be the number of these students having birthday on 14th April. Write down the

probability mass function of X.

Answer 1

Birthday of each student is equally likely to be one of the 365 days of the year.
Therefore, a random student has same probability of having a birthday on each days of a year = 1/365
Let, p = P( a random student has birthday on 14th April)=1/365.
We define a random variable Xi as

Or,


Clearly,


It is know that,


Hence,


Hence, the required probability mass fuction is given by




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