Question: If X and Y are independent binomial random variables with identical parameters n and p, show analytically that the conditional distribution of X given that

If X and Y are independent binomial random variables with identical parameters n and p, show analytically that the conditional of X given that X + Y = m is the hypergeometric Also, give a second argument that yields the same result without any computations.
Suppose that 2n coins are flipped. Let X denote the number of heads in the first n flips and Y the number in the second n flips. Argue that given a total of m heads, the number of heads in the first n flips has the same as the number of white balls selected when a sample of size m is chosen from n white and n black balls.

Step by Step Solution

★★★★★

3.48 Rating (174 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

PX k X Y m PX ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

588-M-S-C-R-V (784).docx

120 KBs Word File

Students Have Also Explored These Related Statistics Questions!

Let X and Y be independent binomial random variables with parameters (n, p1) and (m, p2), respectively. (a) Find E (X/n Y/n) (b) Find Var (X/n Y/n) (c) Show that (x/n Y/n) ~ N (E(Y/n Y/n), Var...

Let X and Y be independent binomial random variables with parameters (m, p) and (n, p), respectively. Use the mgfs to show that X+Y is a binomial random variable with parameters m + n and p.

If X and Y are any two random variables, then the covariance of X and Y is defined by Cov(X, Y) = E ((X E(X))(Y E(Y ))). That Cov(X, X) = V (X). Show that, if X and Y are independent, then Cov(X, Y)...

15. If X and Y are independent binomial random variables with identical parameters n and p, show analytically that the conditional distribution of X, given that X+Y=m, is the hypergeometric...

If X and Y are independent binomial random variables with identical parameters n and p. i) Identify the conditional pmf of X given that X + Y = m. Provide the name and parameters of the corresponding...

Let X, Y, Z be (respectively) the number of nights that Alice, Bob, and Charlotte eat in the dining hall during a 7-day week. Assume that X, Y, Z are independent Binomial random variables that each...

Let X and Y be independent binomial random variables with parameters (m, p) and (n, p), respectively. Let W = X + Y. (a) Derive the probability mass function of W directly from the joint proba-...

What are the fundamental differences between trademarks, copyrights, and patents? What are some ways a business can protect its intellectual property?

3.8. Let X and Y be independent binomial random variables having parameters (N, p) and (M, p), respectively. Let Z = X + Y. (a) Argue that Z has a binomial distribution with parameters (N + M, p) by...

Find the below requirements is business case for a stand alone solar powered cooker that will provide 4 hours cooking per day for a family group. assume 11 hours of regular sunlight. as well as...

You own 400 shares of a stock that is trading at $25 per share. You find on the market a put option on this share trading at $6.25 with a beta of 0.5. You are afraid the stock price can go down in...

On January of the current year, Missy ( 1 7 \ % ) , Davis ( 3 3 \ % ) , and Dianna ( 5 0 \ % ) are partners in the MDSS Partnership. During the current year, MDSS reports the following results. View...

Let A be a square matrix such that ATA = I. Show that |A| = 1.

2. Suppose that the number of events that occur in a given time period is a Poisson random variable with parameter A. If each event is classified as a type i event with probability p,, i = 1, n. p, =...

1,..., n, are independent Poisson random variables with respective parame- ters Ap, i 1,...,n.

3. Suggest a procedure for using Buffon's needle problem to estimate w. Surpris- ingly enough, this was once a common method of evaluating w.

ADVANCED BUSINESS STATISTICS HOMEWORK Prepare a bar chart for the data in the following table. This hypothetical table shows the number of home runs hit in 2017 by these three baseball players. The...

Suppose a 6-sided die is weighted to create the following probability distribution. Determine P(4). Outcome 1 2 3 Probability 0.07 0.27 0.1 4 Let E be the event of rolling an even number. Determine...

On January 1, 2021, Canseco Plumbing Fixtures purchased equipment for $44,000. Residual value at the end of an estimated four-year service life is expected to be $8,000. The company expects the...