Question

a. Suppose that A and B are two independent integer-valued random variables with P(A=k)=(n1 choose k)pk(1-p)n1-k...

a. Suppose that A and B are two independent integer-valued random variables with P(A=k)=(n1 choose k)pk(1-p)n1-k and P(B=k)=(n2 choose k)pk(1-p)n2-k for some positive integers n1 and n2. Write (and simplify) a formula for P(A=k | A+B=m). For which values of k is this probability nonzero?

b. A sample of m balls is drawn (without replacement) from an urn containing n1 white balls and n2 black balls. Let W be the number of white balls in the sample. Write a formula for P(W=k).

c. Your answer for part a and b should be the same. Explain why this is.(Hint: Interpret the variables A and B in the context of coin flips, and interpret the conditional probability computed in part a in terms of those coin flips.)

Homework Answers

Answer #1

W follows hypergeometric distribution with parameter{ (n1+n2),n2,m}

n1+n2 range {1,2.....}

n2 range {1,2.....}

m range {1,2.....( n1+n2)}

(C). Answer for part a and part b are same.

Let variable A indicates flip of a coin with event n1 and B also indicates flip of another coin with event n2. Therefore (n1+n2) be the sum of events from where m sample drawn. If there are k sample is drawn from n1 events then (m-k) sample is drawn from n2 events. It is a conditional part which is similar to part b. We know that 'with replacement' sample follows binomial distribution and 'without replacement ' follows hypergeometric distribution of same sample.... And the conditional distribution of binomial distribution of two variable follows hypergeometric distribution. Thats way the answer of part a and part b are same.

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT