Question

Given a random variable X~exp(5). Z=(X-2)3 1. Find the distribution function FZ(t). 2. Find fz(t).

Given a random variable X~exp(5). Z=(X-2)3

1. Find the distribution function FZ(t).

2. Find fz(t).

Homework Answers

Answer #1

TOPIC:Transformation of random variables.

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
5. Consider the random variable X with the following distribution function for a > 0, β...
5. Consider the random variable X with the following distribution function for a > 0, β > 0: FX (z) = 0 for z ≤ 0 ​= 1 – exp [–(z/a)β] for z > 0 (where exp y = ey) (a) Determine the inverse function of FX (z), where 0 < z < 1. (b) Let a = β = 2 for the random variable X, and define the numbers u1 = .33 and u2 = .9. Use the inverse...
Poisson Distribution: p(x, λ)  =   λx  exp(-λ) /x!  ,  x = 0, 1, 2, ….. Find the moment generating function Mx(t)...
Poisson Distribution: p(x, λ)  =   λx  exp(-λ) /x!  ,  x = 0, 1, 2, ….. Find the moment generating function Mx(t) Find E(X) using the moment generating function 2. If X1 , X2 , X3  are independent and have means 4, 9, and 3, and variencesn3, 7, and 5. Given that Y = 2X1  -  3X2  + 4X3. find the mean of Y variance of  Y. 3. A safety engineer claims that 2 in 12 automobile accidents are due to driver fatigue. Using the formula for Binomial Distribution find the...
X is a random variable with Moment Generating Function M(t) = exp(3t + t2). Calculate P[...
X is a random variable with Moment Generating Function M(t) = exp(3t + t2). Calculate P[ X > 3 ]
Find the conditional mean and conditional variance of the random variable given the pdf: exp(-x)u(x) given...
Find the conditional mean and conditional variance of the random variable given the pdf: exp(-x)u(x) given X>1
The random variable X has moment generating function ϕX(t)=exp((9t)^2)/2)+15t) Provide answers to the following to two...
The random variable X has moment generating function ϕX(t)=exp((9t)^2)/2)+15t) Provide answers to the following to two decimal places (a) Evaluate the natural logarithm of the moment generating function of 2X at the point t=0.62. (b) Hence (or otherwise) find the expectation of 2X. c) Evaluate the natural logarithm of the moment generating function of 2X+7 at the point t=0.62.
A random variable X has its probability function given by x 0 1 2 3 4...
A random variable X has its probability function given by x 0 1 2 3 4 f(x) 0.3c 0.1c c 0.2c 0.4c a) Find c and F(x), the cumulative distribution function for X (for all real values of X). b) Find the probabilities of the event X = 6 and the event X >= 4. c) Find P(1 < X <= 4) and P(1 < X <= 4 | X <= 3).
The density function of random variable X is given by f(x) = 1/4 , if 0...
The density function of random variable X is given by f(x) = 1/4 , if 0 Find P(x>2) Find the expected value of X, E(X). Find variance of X, Var(X). Let F(X) be cumulative distribution function of X. Find F(3/2)
Let X be a random variable with probability mass function P(X =1) =1/2, P(X=2)=1/3, P(X=5)=1/6 (a)...
Let X be a random variable with probability mass function P(X =1) =1/2, P(X=2)=1/3, P(X=5)=1/6 (a) Find a function g such that E[g(X)]=1/3 ln(2) + 1/6 ln(5). You answer should give at least the values g(k) for all possible values of k of X, but you can also specify g on a larger set if possible. (b) Let t be some real number. Find a function g such that E[g(X)] =1/2 e^t + 2/3 e^(2t) + 5/6 e^(5t)
A random variable X has the cumulative distribution function (cdf) given by F(x) = (1 +...
A random variable X has the cumulative distribution function (cdf) given by F(x) = (1 + e−x ) −1 , −∞ < x < ∞. (i) Find the probability density function (pdf) of X. (ii) Roughly, take 10 points in the range of x (5 points below 0 and 5 points more than 0) and plot the pdf on these 10 points. Does it look like the pdf is symmetric around 0? (iii) Also, find the expected value of X.
Given a random variable X following normal distribution with mean of -3 and standard deviation of...
Given a random variable X following normal distribution with mean of -3 and standard deviation of 4. Then random variable Y=0.4X+5 is also normal. (1)Find the distribution of Y, i.e. μy,σy (2)Find the probabilities P(−4<X<0),P(−1<Y<0) (3)Find the probabilities(let n size =8) P(−4<X¯<0),P(3<Y¯<4) (4)Find the 53th percentile of the distribution of X
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT