6.Let X be a random variable taking values in (0,∞) with proba-bility density functionfx(u) = 5e5uu > 0.Total marks 8Let Y = X2. Find the probability density function of Y.[8 Marks]

Let's give it a try. To provide precise answer, I believe further reference is necessary, but I will…

Answered: 6. Let X be a random variable taking…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 21E

See similar textbooks

Question

6.
Let X be a random variable taking values in (0,∞) with proba-
bility density function
fx(u) = 5e5u
u > 0.
Total marks 8
Let Y = X2. Find the probability density function of Y.
[8 Marks]

Expert Solution

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Similar questions

Let X be a random variable with uniform distribution on the interval [-2,2]. Let Y be defined as Y = X5. Calculate the pdf of Y.
Let X be a Gaussian random variable with zero mean and variance equal to 2. 1-Find the probability density function of the random variableY = 4X + 4 2-Find the probability P(Y>4).
2. Let X be a random variable with density function ) = √(2x² - + f(x) = Find the expected value of g(x) = 2X+1. 8x2 +5x + 6), 1 < x < 2, 0, elsewhere
Let X be a continuous random variable with PDF 3 x > 1 x4 fx(x) = otherwise Find the mean and variance of x.
36. QUESTION: Let X have the density f(x) = 2x if 0 < r <1 and f(x) = 0 otherwise. Show that X has the mean 2/3 and the variance 1/18. Find the mean and the variance of the random variable Y = -2X + 3.
Q4) The probability mass function of Y is f(y) = y/6 for y=1,2,3,4. Find the variance of Y.
The plot below shows the probability density functions (PDFS) of three continuous random variables: X, Y, and Z.
Let X and Y are two random variables with p.d.f as F(x,y) = 3x^2y+3xy^2,0 < x< 1,0 < y < 1. (i) Find conditional density of X given Y. (ii) Find the mean, mode and standard deviation of r.v Y. (iii) Correlation between X and Y. (iv) Check that X and Y are independent or not?
3. CLO4 Let X be a continuous random variable with probability density function (pdf) Ix(x)= (2r 0≤x≤1 0 otherwise and let the random variable Y given X = r be uniformly distributed on [-x,x]. (a) Obtain the marginal probability density function of Y. MAT 263 Probability Theory Assignment 2- Page 3 of 3 NSAN (b) Compute Cor(X, Y). (c) Compute P(Y|
2. Suppose that the random variable X possess a uniform distribution on the interval (0, 1). Let U=X. Find the marginal probability density function of U using the distribution function method.
6. Assume that X is a continuous random variable with probability density function (pdf) 6. { (I+2) 27 if -2
Let X be a random variable with pdf: f(x)= k(10 - 2x) for x being [0,5] a.) Find k b.) Find E(X) c.) Find Var(X) d.) Find E(3 *squareroot(X))

SEE MORE QUESTIONS

Recommended textbooks for you

Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage

SEE MORE TEXTBOOKS

6. Let X be a random variable taking values in (0,∞) with proba- bility density function fx(u) = 5e5u u > 0. Total marks 8 Let Y = X2. Find the probability density function of Y. [8 Marks]