Solution Found!
Suppose that n independent tosses of a coin having
Chapter 4, Problem 15TE(choose chapter or problem)
Problem 15TE
Suppose that n independent tosses of a coin having probability p of coming up heads are made. Show that the probability that an even number of heads results is , where q − 1− p. Do this by proving and then utilizing the identity
where [n/2] is the largest integer less than or equal to n/2. Compare this exercise with Theoretical Exercise of Chapter 3.
Exercise
(a) Prove that if E and F arc mutually exclusive, then
(b) Prove that if Ei,i ≥ 1 are mutually exclusive, then
Questions & Answers
QUESTION:
Problem 15TE
Suppose that n independent tosses of a coin having probability p of coming up heads are made. Show that the probability that an even number of heads results is , where q − 1− p. Do this by proving and then utilizing the identity
where [n/2] is the largest integer less than or equal to n/2. Compare this exercise with Theoretical Exercise of Chapter 3.
Exercise
(a) Prove that if E and F arc mutually exclusive, then
(b) Prove that if Ei,i ≥ 1 are mutually exclusive, then
ANSWER:
Solution 15TE
Step1 of 2:
From the given problem we have n independent tosses of a coin having probability p of coming up heads are made.
We need to prove that
Step2 of 2:
Consider,
Applying binomial theorem to each of the terms of the right side of the equation
Take n-k = j in the right sum, then we get: