Question: Let X1, X2, . . . , Xn be a random sample from a Poisson distribution with mean > 0. Find the conditional probability

Let X1, X2, . . . , Xn be a random sample from a Poisson with mean λ > 0. Find the conditional probability P(X1 = x1, . . . , Xn = xn | Y = y), where Y = X1 + · · · + Xn and the nonnegative integers x1, x2, . . . , xn sum to y. Note that this probability does not depend on λ.

Step by Step Solution

★★★★★

3.43 Rating (169 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

The distribution of Y is Poisson with me... 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)

579-M-S-P-E (711).docx

120 KBs Word File

Students Have Also Explored These Related Statistics Questions!

(a) Let X1, . . ., Xn be a random sample from a Poisson distribution with parameter Î». Derive a (1 Î±) 100% large sample confidence interval for Î». (b) To date...

a. Let X1 have a chi-squared distribution with parameter n1 (see Section 4.4), and let X2 be independent of X1 and have a chi-squared distribution with parameter v2. Use the technique of Example 5.22...

Let X1, X2, . . ., Xn be a random sample from a distribution with unknown mean m and variance 2. Show that the method of moments estimators for m and 2 are, respectively, the sample mean and Note...

5. Let (X1, X2, . .., Xn) be a random sample from a Poisson()) distribution where A is an unknown parameter. (a) Suppose that the sample size n is large. Find a pivotal variable in terms of the...

Let X1, X2, ..., Xn be a random sample from a Poisson distribution with mean 1. Thus, Y = = X; has a Poisson distribution with mean n1. Moreover, by the Central limit Theorem, X = Y has,...

Hi I'm stuck this problem and I need correct answer asap. thank you Let X1, X2, ..., Xn denote a random sample from a Poisson distribution that has the mean 0 > 0. Note that if X ~ Poi(0) then its...

please help with practice problem 5. Let X1, X2, ..., Xn be a random sample from the Poisson distribution with mean 0 (> 0). For estimation 0, consider the following three estimators 01 = = Er-1 Xi,...

Question 4: 1. Let X1, X2, . . . ,Xn be a random sample from an Uniform distribution on [0, 9]. Find an estimator for 0 using the method of moments (2pts). Is this estimator unbiased? Explain (lpt)....

1. Let (X1, X2, ..., Xn) be a random sample from an exponential distribution with probability density function f(x) given by Ae-" for x > 0; f (ac) = 0 , otherwise. (a Find the moment estimator A of...

Let X1, X2, . . . , Xn be a random sample from a gamma distribution with known and with = 1/. Say has a prior pdf that is gamma with parameters 0 and 0, so that the prior mean is 00. (a) Find the...

A number of alternative entry modes were identified in the chapter. Locate a company that uses indirect export and one using direct export. Describe their market entry strategies and determine why...

Given the system of equations 3x2 + 7x3 = 2 x1 + 2x2 x3 = 3 5x1 2x2 = 2 (a) Compute the determinant. (b) Use Cramers rule to solve for the xs. (c) Use Guess elimination with partial pivoting to...

2.86 What is the difference between a drill-down and a slicer?

What is the difference between the strong and weak theory of advertising effectiveness?

Consider the following probabilities: P (A) = 0.40, P (B) = 0.50 and P (Ac Bc) = 0.24. Find: a. P (Ac | Bc) b. P (Ac Bc) c. P (A B)

Survey data, based on 65,000 mobile phone subscribers, shows that 44% of the subscribers use smart-phones (Forbes, December15, 2011). Moreover, 51% of smart-phone users are women. a. Find the...

Twenty percent of students in a college ever go to their professor during office hours. Of those who go, 30% seek minor clarification and 70% seek major clarification. a. What is the probability that...

Harrimon Industries bonds have 6 years left to maturity. Interest is paid annually, and the bonds have a $1,000 par value and a coupon rate of 9%. What is the yield to maturity at a current market...

Liala created a portfolio with $96,000 invested equally in 3 securities security A has a return of 8%, security B has a return of -0.5 and security C has a return of 10%. find the return for this...

Please refer to the following iamge Question 1: (15 marks) Waiting for a bus is modeled as a continuous Uniform random variable that can take on any value between 0 to 20 minutes. Let X= waiting time...