Question

The geometric distribution with parameter p represents the number of failures in a sequence of independent...

The geometric distribution with parameter p represents the number of failures in a sequence of independent Bernoulli trials before a success occurs. Show that this distribution is of the exponential family.

Math   Statistics-And-Probability   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Let {Xn} be a sequence of random variables that follow a geometric distribution with parameter λ/n,...
Let {Xn} be a sequence of random variables that follow a geometric distribution with parameter λ/n, where n > λ > 0. Show that as n → ∞, Xn/n converges in distribution to an exponential distribution with rate λ.
Match the distribution to the description Group of answer choices Bernoulli Binomial   Geometric      Negative Binomial...
Match the distribution to the description Group of answer choices Bernoulli Binomial   Geometric      Negative Binomial Poisson Counting the number of occurrences of an event in a continuous interval            the sum of n independent bernoulli trials            given a series of independent bernoulli trials, stop when you get r successes (where r can be any positive integer)            given a series of independent bernoulli trials, stop when you get the first success     ...
Consider a succession of independent Bernoulli tests of parameter p. Let X be the number of...
Consider a succession of independent Bernoulli tests of parameter p. Let X be the number of failure before the first success and Y the number of failure between the first success and the second. a) Calculate the joint density function of X and Y. b) Calculate the conditional density function of X given Y = y. c) Calculate the conditional density function of Y given X = x. d) Are the variables X and Y independent? Argue your answer.
Determine the CDF of Geometric Distribution with parameter p.
Determine the CDF of Geometric Distribution with parameter p.
5. If X and Y are independent geometric RVs with parameters p and r re- spectively,...
5. If X and Y are independent geometric RVs with parameters p and r re- spectively, show that U = min(X, Y ) is geometric with parameter p + r − rp = 1−(1−r)(1−p).
Suppose Y_1, Y_2,… Y_n denote a random sample of a geometric distribution with parameter p. Find...
Suppose Y_1, Y_2,… Y_n denote a random sample of a geometric distribution with parameter p. Find the maximum likelihood estimator for p.
Consider a sequence of independent trials of an experiment where each trial can result in one...
Consider a sequence of independent trials of an experiment where each trial can result in one of two possible outcomes, “Success” or “Failure”. Suppose that the probability of success on any one trial is p. Let X be the number of trials until the rth success is observed, where r ≥ 1 is an integer. (a) Derive the probability mass function (pmf) for X. Show your work. (b) Name the distribution by matching your resulting pmf up with one in...
. Consider the Bernoulli distribution, P(X = x|p) = (p^x) (1 − p) ^(1−x) for x...
. Consider the Bernoulli distribution, P(X = x|p) = (p^x) (1 − p) ^(1−x) for x = 0 and x = 1. (a) Show that this is an exponential family. (b) Find a sufficient statistic for p. (c) Show that X is a m.v.u.e. for p.
Suppose that X|λ is an exponential random variable with parameter λ and that λ|p is geometric...
Suppose that X|λ is an exponential random variable with parameter λ and that λ|p is geometric with parameter p. Further suppose that p is uniform between zero and one. Determine the pdf for the random variable X and compute E(X).
a is a random variable which follows geometric distribution, with parameter p = 0.1. b =...
a is a random variable which follows geometric distribution, with parameter p = 0.1. b = ln(a) 1. what is the probability mass function of b. 2 Prob (b> ln(3)) = ?
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT