Question: The Laplace distribution, also known as the double exponential distribution, has density function proportional to e |x| for all real x. Find the mean and

The Laplace distribution, also known as the double exponential distribution, has density function proportional to e^−|x| for all real x. Find the mean and variance of the distribution.

Step by Step Solution

★★★★★

3.59 Rating (167 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

First solve for the constant of proportio... 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

Students Have Also Explored These Related Probability With Applications Questions!

A double exponential distribution, often called a Laplace distribution, has a probability density function for - oo (a) P(X (b) P(X > 1) f(x) =;re

In Example 7.2.16 we saw that the normal distribution is its own conjugate family. It is sometimes the case, however, that a conjugate prior does not accurately reflect prior knowledge, and a...

Let X1,..., Xn be iid n(,2), 2 known, and let have a double exponential distribution, that is, () = e-|0|//(2a), a known. A Bayesian test of the hypotheses H0: 0 versus H1: > 0 will decide in...

Table of z values and probabilities for the standard normal distribution. z is the first column plus the top row. Each cell shows P( X z). For example P( X 1.04) = .8508. For z

Accidental poisoning of children is a great concern to the Poison Control Center. From the past, 12.5% of all children reported with accidental poisoning required hospitalization. For the years 1993...

2. Brian is monitoring the number of users playing Vegetable Crossing after the latest round of bug fixes. He finds that the number of active users on a given day can be modeled as a normal...

10. Please Answer 1. Suppose a continuous random variable X has the following probability density function: f(x) + 2 X What is the probability P(OsXs1) ? What is the probability P(OsX=0.5) ? 2....

Suppose that the underlying distribution function is symmetric, thus the mean is the same as the median, = m, representing the center. Suppose that we are interested in testing m(= ) = 75 against m >...

i need an example done for me for probability of a defect and setting a variancd reduction target for slides. any sort of problem is fine. 9.2.2 Predicting the Probability of a Defect Knowing the...

Refer to the Pizza Vesuvio company information in Cornerstone Exercise 3-16. Coefficients shown by a regression program for this data are: Intercept ......1,145 X Variable ......13.82 Required: Use...

Tracy is preparing her budget for next year and needs your assistance. Now that she has a better idea of what to expect now that she is in business full time, we want to begin having some of her...

Exercise 1 2 - 1 7 ( Algorithmic ) ( LO . 2 ) Compute the 2 0 2 4 AMT exemption for the following taxpayers: Round final answer to the nearest dollar. If an amount is zero, enter " 0 " . Click here...

9. How do investment professionals, such as stockbrokers or financial planners, help investors?

1. Draw 100 random samples from a binomial distribution with parameters n = 10 and p = .4. Consider an approximation to this distribution by a normal distribution with mean = np = 4 and variance =...

What is the exact probability distribution of the position of the balls at the bottom with respect to the entry position (arbitrarily denoted by 0)? SIMULATION An apparatus displaces a collection of...

Can you think of an approximation to the distribution derived in Problem 5.78? SIMULATION An apparatus displaces a collection of balls to the top of a stack by suction. At the top level (Level 1)...

Kentucky Hardware Company (KHC) is considering an investment project that requires a new machine for producing special tools. This new machine costs $1,000,000 and will be depreciated over 10 years...

The characteristic polynomial of a 5 5 matrix is given below. Find the eigenvalues and their multiplicities. Question 5 {1 point] The characteristic polynomial of a 5 x 5 matrix is giyen below. Find...

Find the mean hours of exercise per week by the participants. Find the variance of the hours of exercise per week by the participants. Determine if there is a linear relationship between the hours of...