Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

Let $X$ have a Weibull distribution with parameters $\alpha=2$ and $\beta .$ Show that $Y=2 X^{2} / \beta^{2}$ has an exponential distribution with $\lambda=1 / 2$

Intro Stats / AP Statistics

Chapter 3

Continuous Random Variables and Probability Distributions

Section 9

Supplementary Exercises

Continuous Random Variables

University of North Carolina at Chapel Hill

Cairn University

Idaho State University

Lectures

05:39

Let $X$ and $Y$ be indepen…

03:47

Let $X_{1}, \ldots, X_{n}$…

07:23

(a) Suppose the lifetime $…

04:00

If $X$ is distributed as $…

04:21

(a) Use mgfs to show that …

03:46

Suppose the distribution o…

02:57

Suppose $f$ is a probabili…

01:13

Determine the cumulative d…

02:15

02:07

04:43

The formula for finding th…

00:14

Find the equation for the …

01:32

Consider $\quad$ two $\qua…

02:00

Let $X$ be a Bernoulli rv …

03:25

Verify that the functions …

05:06

Find the expected value, t…

05:55

03:27

Show that for large values…

07:54

Let $X_{1}, X_{2}, \ldots,…

01:54

Show that the density func…

we're told that X follows a Waibel distribution with parameters. Alfa equals two and beta were also given a transformation. Why equals two times X squared, divided by beta. And we want to show that why is an exponential random variable with parameter lambda equals half. Now the CDF of the Waibel distribution is given by this equation so we could begin by starting with the CDF for why? So this transformation should actually have a beta squared in the denominator. So this is equal to the probability that excess lesson or equal to you data times y over to to the explain it one half. So this is the cumulative distribution for for X at this value. So if we plug this value into ex into the CDF four x, we get the following in terms of the domain. If X is greater than or equal to zero, that means why must be greater than or equal to zero as well. So we have just found the CDF for why and the CDF for an exponential random variable is one minus e to the exponents, Negative lambda and therefore why is an exponential random variable with lambda is equal to one half

View More Answers From This Book

Find Another Textbook

Numerade Educator

Let $X$ and $Y$ be independent gamma random variables, both with the same sc…

Let $X_{1}, \ldots, X_{n}$ be a random sample from a gamma distribution with…

(a) Suppose the lifetime $X$ of a component, when measured in hours, has a g…

If $X$ is distributed as $N(\mu, \sigma),$ find the pdf of $Y=e^{X} .$ Verif…

(a) Use mgfs to show that if $X$ has a normal distribution with parameters $…

Suppose the distribution of the time $X$ (in hours) spent by students at a c…

Suppose $f$ is a probability density function for the random variable $X$ wi…

Determine the cumulative distribution function for the exponential distribut…

Let $X_{1}, \ldots, X_{n}$ be a random sample from the uniform distribution …

The formula for finding the variance for a probabilitydistribution is

Find the equation for the standard normal distribution by substituting 0 for…

Consider $\quad$ two $\quad$ wave $\quad$ functions.$$y_{1}(x, t)=A \sin (k …

Let $X$ be a Bernoulli rv with pmf as in Example $2.17 .$(a) Compute $E\…

Verify that the functions are probability density functions for a continuous…

Find the expected value, the variance, and the standard deviation, when they…

Show that for large values of $\lambda$ the Planck distribution, Eq. $(38.32…

Let $X_{1}, X_{2}, \ldots, X_{n}$ represent a random sample from a Rayleigh …

Show that the density function $p(x)=\frac{2}{\pi\left(x^{2}+1\right)}$ on $…

03:00

Assume a finite population has 10 elements. Number the elements from 1 to 10…

04:09

If a measurement error $X$ is distributed as $N(0,1),$ find the pdf of $|X|,…

03:57

If $X \sim$ Unif[0, 1], find a linear transformation $Y=c X+d$ such that $Y$…

02:42

When $X_{1}, X_{2}, \ldots, X_{n}$ are independent Poisson variables, each w…

02:18

Suppose you have a random sample $X_{1}, X_{2}, \ldots, X_{n}$ from the Pois…

06:55

Exercise 39$($ Sect. 2.3$)$ describes the game Plinko from The Price is Righ…

08:10

Aphid infestation of fruit trees can be controlled either by spraying with p…

04:01

A manufacturer of nickel-hydrogen batteries randomly selects 100 nickel plat…

10:22

Data from the U.S. Census Bureau provides the population by state in million…

02:04

The manager of an automobile dealership is considering a new bonus plan desi…