How to find the probability and generating function for this problem? We toss a coin k times which

madridomot

madridomot

Answered question

2022-05-20

How to find the probability and generating function for this problem?
We toss a coin k times which is having probability p of landing on heads and a probability q = 1 p of landing on tails. The probability of getting exactly n heads is denoted by a n . What is a n and the generating function of the sequence ( a n )?

Answer & Explanation

Leah Conley

Leah Conley

Beginner2022-05-21Added 12 answers

Step 1
The pmf is ( k n ) p n q k n ,   n { 0 , 1 , . . . , k }.
Step 2
It follows that the generating function is n = 0 k e n t ( k n ) p n q k n = n = 0 k ( k n ) ( p e t ) n q k n
Now use the binominal theorem.

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