Question: 16. The random variable X is said to be a Laplace random variable or double exponentially distributed if its probability density function is given by

16. The random variable X is said to be a Laplace random variable or double exponentially distributed if its probability density function is given by

f(x)=ce-, -xxx.

(a) Find the value of c.

(b) Prove that E(X2n) = (2n)! and E(X2n+1) = 0.

f(x)=ce-, -xxx.

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock blur-text-image
Question Has Been Solved by an Expert!

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

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Probability And Stochastic Modeling Questions!

Q:

State if the following statements are true or false by reporting ``T'' (for ``true'') or ``F'' (for ``false'') in the parentheses after the end of the sentence. 1. If the expected value of sample...

Q:

The cumulative distribution function of a random variable X is given by F(x) = 0; if x Find the probability density function of x and P(- /2

Q:

The cumulative distribution function of a random variable X is given by F(x) = 0; if x Find the probability density function of x and P(- /2

Q:

12. Here are summary statistics for randomly selected weights of newborn? girls: n=36?, x=3180.6?g, s=700.5g. Use a confidence level of 90?% to complete parts? (a) through? (d) below. a. Identify the...

Q:

12. Here are summary statistics for randomly selected weights of newborn? girls: n=36?, x=3180.6?g, s=700.5g. Use a confidence level of 90?% to complete parts? (a) through? (d) below. a. Identify the...

Q:

5. (15 points) Let X be a random variable with cumulative distribution function 0 x1 a. Find P(-1 2X, . b. Find the marginal probability density function of X, . c. Find EX,X2. d. Find EXI. 9. (10...

Q:

2. As defined in Exercise 16, Section 7.3, a random variable X is said to be Laplace, if its probability density function is given by Let U and V be independent and identically distributed...

Q:

A random variable X is said to have a chi-squared distribution on v degrees of freedom if it has the same distribution as whcre Z 1 , Z 2 , ... , Z v are independent standard normal variates. Use the...

Q:

1.)Use the given statement to represent a claim. Write its complement and state which is H0 and which is Ha. 14 Find the complement of the claim. less than or equals not equals less than

Q:

1.)Find the complement of the claim. >406 Which is H0 and which is Ha? 2.)Use the given statement to represent a claim. Write its complement and state which is H0 and which is Ha. p>0.57 Find the...

Q:

The figure below shows the path of an optical ray passing through a stack of three layers with respective indices: nt- 1.5, n2 - 13 and n3-nt. The light enters the middle layer at point A with an...

Q:

Project Description: Topic: Mobile Computing, the emerging technology (Find the attachment other open sources can also be considered) . After selecting the topic, read about it , analyze it, and...

Q:

$ 6 0 0 Mark for follow up Question 7 of 8 5 . Brady received interest from several different sources. Which of the following types of interest is nontaxable on a q , Interest income from municipal...

Q:

Which eye do you use more? To test which you favor, hold a finger up at arm's length. With both eyes open, look past it at a distant object. Now close your right eye. If your finger appears to jump...