Question

In Example 6.33 we found the distribution of the sum of two i.i.d. exponential variables with...

In Example 6.33 we found the distribution of the sum of two i.i.d. exponential variables with parameter λ. Call the sum X. Let Y be a third independent exponential variable with parameter λ. Use the convolution formula 6.8 to find the sum of three independent exponential random variables by finding the distribution of X + Y.

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 X and Y be independent random variables following Poisson distributions, each with parameter λ =...
Let X and Y be independent random variables following Poisson distributions, each with parameter λ = 1. Show that the distribution of Z = X + Y is Poisson with parameter λ = 2. using convolution formula
Assume that X and Y are independent random variables, each having an exponential density with parameter...
Assume that X and Y are independent random variables, each having an exponential density with parameter λ. Let Z = |X - Y|. What is the density of Z?
X and Y ar i.i.d. exponential random variables with mean = 2. Let Z = X...
X and Y ar i.i.d. exponential random variables with mean = 2. Let Z = X + Y. The probability that Z is less than or equal to 3 is:
Let X and Y be independent exponential random variables with respective rates ? and ? Is...
Let X and Y be independent exponential random variables with respective rates ? and ? Is max(X, Y ) an exponential random variable?
Let S4 = X1 + ... + X4 is the sum of 4 independent random variables,...
Let S4 = X1 + ... + X4 is the sum of 4 independent random variables, and each Xi is exponential with λ = 3. Find the moment generating function m(t) for S4. Also find m′(0) and m′′(0）
(14pts) Let X and Y be i.i.d. geometric random variables with parameter (probability of success) p,...
(14pts) Let X and Y be i.i.d. geometric random variables with parameter (probability of success) p, 0 < p < 1. (a) (6pts) Find P(X > Y ). (b) (8pts) Find P(X + Y = n) and P(X = k∣X + Y = n), for n = 2, 3, ..., and k = 1, 2, ..., n − 1.
Using the convolution formula for the sum of random variables, determine and plot the probability density...
Using the convolution formula for the sum of random variables, determine and plot the probability density function of the average of 2 independent random variables which have identical uniform distributions. Now find the density of the average of 2 independent instances of the random variable you obtained previously. Iterate the procedure a few times, and observe the resulting probability density.
Convolution of distribution integral range 1.Example: Exponential distribution convolution fx+y(z)=intergral from 0 to z fx(x)fy(z-x))dx how...
Convolution of distribution integral range 1.Example: Exponential distribution convolution fx+y(z)=intergral from 0 to z fx(x)fy(z-x))dx how we get the range 0 to z??? Better to use mathematics and a graph to explain. Also, when it ask find the density function X+Y, should I just add two exponential density function together?
Let X denote a random variable that follows a binomial distribution with parameters n=5, p=0.3, and...
Let X denote a random variable that follows a binomial distribution with parameters n=5, p=0.3, and Y denote a random variable that has a Poisson distribution with parameter λ = 6. Additionally, assume that X and Y are independent random variables. Derive the joint probability distribution function for X and Y. Make sure to explain your steps.
The random variables X and Y are independent. X has a Uniform distribution on [0, 5],...
The random variables X and Y are independent. X has a Uniform distribution on [0, 5], while Y has an Exponential distribution with parameter λ = 2. Define W = X + Y. A.    What is the expected value of W? B.    What is the standard deviation of W? C.    Determine the pdf of W.  For full credit, you need to write out the integral(s) with the correct limits of integration. Do not bother to calculate the integrals.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT