X, Y and Z are continuous random variables and their joint probabilitydensity functions are defined as follows.Sc(x +2y +32), 0< x, y, z < 1fxYz(x, y, z) =other situations(a) Find the value of C.(b) Find the marginal probability density function fx(x) of X.

Answered: Image /qna-images/answer/1f0a8fe8-98fa-44aa-a197-0ecf8c24aba3.jpg

X, Y and Z are continuous random variables and their joint probability density functions are defined as follows. Sc(x +2y +32), 0 < x, y, z < 1 other situations fxYz(x, y, 2) = (a) Find the value of C. (b) Find the marginal probability density function fx(x) of X.

X, Y and Z are continuous random variables and their joint probability density functions are defined as follows. Sc(x +2y +32), 0 < x, y, z < 1 other situations fxYz(x, y, 2) = (a) Find the value of C. (b) Find the marginal probability density function fx(x) of X.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Related questions

Q: Let X and Y be independent random variables with density ƒ (æ) = 3x² for 0 < x < 1. Then P (X + Y <…

A: Given Information: Let X and Y be independent random variables with the pdf: fx=3x2 ,…

Q: The random variables X and Y are independent to each other. The probability density functions of X,…

A: Given the pdf of the independent random variables X and Y as fXx=2x , 0<x<1 fYy=1 ,…

Q: life lengths of two transistors in an ele uit is a random vector Y ) where X is the life length of…

A: The conditional probability is, P(A| B) = P( A n B) / P(B)

Q: A continuous random variable X has the probability density function 0, hx - h, 3h-hx, 0, which can…

Q: continuous random Variable X has probability Density function defined by f(x) = 5-5x; 0

A: Given: f(x) = 5-5x

Q: Q6. (a) The continuous random variable X has a probability density function given by 2 1 C 2 1< x<2…

Q: Let X and Y has joint probability density function f(X, Y) = 81 - , 0 <x< 3, 0 <y< 3. Find E(X).

A: The joint probability density function is, fX,Y=x2y281,0<x<3,0<y<3

Q: 19. Let X and Y be two random variables with joint probability density function given by fxx(x, y) =…

A: From the given information, f(x,y)=2e-x+yI0,xyI[0,∞)(y) Let us denote X=u and…

Q: The relationship between probability distribution function F(x) and the probability density function…

A: To find whether the given statement is true or false:

Q: Suppose random variables X and Y are conditionally independent given random variable Z, i.e. P(X,…

A: Given that, P(X, Y|Z) = P(X|Z)P(Y|Z) (a). Then P(Y/X,Z)= P(Y,X,Z)/P(X,Z) (X and Y are…

Q: If X is a continuous variable in the range 3 > X > 0 and its distribution function is as follows: F…

Q: (b) Let X and Y have joint probability density function fxx (,)= k, x>0, y > 0, x+y<1 0, otherwise.…

Q: 6) X is a continuous random variable with the following probability density function: fx(x) = 2x,…

A: probability density function of Y=1-X : => fY(y) = 2-2y , 0<y<1Explanation:

Q: Let X be a continuous random variable with probability density function 1 f (x) = 7(1+x² ) Define Y…

A: The mean of Y is given by: μ= E(Y) = E1X It is known that, E1X = ∫-∞∞1xf(x) dx

Q: Let X be a continuous random variable with probability density function f(x) = 2(1-x), 0<=x <= 1.…

A: Given: f(x) = 2(1-x), 0≤x≤1 Y = 2X-1 To find: pdf of Y = ?

Q: Roughly, speaking, we can use probability density functions to model the likelihood of an vent…

Q: For two random variables X and Y, the joint density function is Find (a) the correlation fxy(x, y) =…

Q: Let X be a continuous random variable with density function/ (x)=4e 1. Determine F(5) 2. Determine…

A: Given that the density function is, fx=4e-4x, x>0

Q: 3. Let X be a continuous random variable. Let f(x) = c(x − 1)³ and Sx = [1,3]. Hint: (x - 1)³ = x³ +…

Q: Suppose that the random variables X and Y have the following joint probability density func f(x, y)…

A: Given: fx, y=ce-6xe-3y 0<y<x

Q: function given by

A: Given, X and Y have a joint probability density function fX, Y(x, y)=ce-3x-5yif…

Q: Q6. Let Y be a continuous random variable with the probability density function in the following…

Q: If the joint probability density function of two continuous random variables X and Y is given by f…

Q: Suppose that X is a continuous random variable whose probability density function is given by (4x –…

A: Given:

Q: Suppose that X and Y have a joint probability density function given by ce-3z-5y fxy(x, y) = if x, y…

A: Given f(x,y)=ce-3x-5y x,y≥0

Q: Find a probability density function A continuous random variable X, with mean unity, has probability…

A: Solution

Q: Let Xand Y be two continuous random variables with joint probability density 3x function given by:…

A: The given value are EX=34, EX2=35, EY=38, EY2=15 and EXY=310.

Q: Let Y1 and Y2 be two jointly continuous random variables with joint probability density function f…

A: Given the joint probability density function of continuous random variables Y1 and Y2 as fy1,…

Q: uppose you have the population value 50 and 80 and that their corresponding z-scores respectively.…

A: Given Data: Population value=50 and 80 we also know the corresponding z-score

Q: 7. Let X be a continuous random variable with probability density function given by Se-(z-z0) x > x0…

A: Let X be the continuous random variable with probability density function is, f(x) = { e^-(x-x0)…

Q: function given by 3x4. x 21, Sx(x) = 0, otherwise. A new random variable Y is defined by the…

Q: where , & are positive constants. (a) Find the value of a. (b) Consider the transformation X = WP,…

Q: Suppose that X and Y have a joint probability density function given by fxx(1, y) = if 1, y 2 0…

A: A joint probability density function gives the probability for two random variables. For example two…

Q: 6 A continuous random variable T (in years) of the lifespan of a device has the foll probability…

A: Provided information is, a continuous random variable T (in years) of the lifespan of device has…

Q: c) Let S and T be two independent random variables with probability density functions 1 f(s) =- s >…

Q: . Let X and Y be continuous random variables with joint probability density function given by Sc,…

A: Let and be continuous random variables with joint probability density function is given byWhere,…

Q: The joint probability mass function of X and Y is given by (x₁²y₁ P(X = x₁, Y = y) = Pxy(x) = 30 0 x…

A: Joint probability mass function of X and Y is given as: PX=xi,Y=yi=xi2 yi30, xi=1,2 ; yi=1,2,3

Q: 8)Let X1, X2, ..., Xn be a sample of n units from a population with a probability density function f…

A: Let, Y1,...,Y7 be order statistics . The pdf of X is, f(x|θ)=θxθ-1 ; 0<x<1, θ>0 The CDF for…

Question

100%

X, Y and Z are continuous random variables and their joint probability
density functions are defined as follows.
Sc(x +2y +32), 0< x, y, z < 1
fxYz(x, y, z) =
other situations
(a) Find the value of C.
(b) Find the marginal probability density function fx(x) of X.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

BIT A

VIEW

BIT B

VIEW

Step by step

Solved in 3 steps with 6 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Multivariate Distributions and Functions of Random Variables$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.

Similar questions

The probability density function of a variate X is as follows, 1 2 3 4 P(X) k 3k 5k 7k 9k 11k 13k Find the value of, (i) k (ii) P(X < 4) (iii) P(3 < X < 6).
a) Let X be a continuous random variable with the following probability density function (2x3 f(x)={11 2 +5) , 0
5. Let 0 and a be parameters. Show that the family of functions fo,a(x) = I > 0 (x+0)a+1³ is a probability density function. What can you say about the mean of a random variable that has fo,a as a pdf?
7. Let X and Y denote two continuous random variables. Let f(x,y) denote the joint probability density function and fx(x) and fy (y) the marginal probability density functions for X and Y, respectively. Finally let Z = aX + bY, where a and b are non-zero real numbers. (e) Derive an expression for Cov(Z) as a function of Var (X), Var(Y) and Cov(X,Y). [You may use standard results relating to variance and covariance without proof, but these should be clearly stated.]
A continuous random variable has probability density function given by K(2x-3);1<x2 Find k if f(x) is a probability density function
fx(x) is a probability density function such that fx(x) = {a(2 - x) 0 k), please find k. %3D O a. 1+(2/V2) O b. 2+(1//2) O c. 1+(1//2) O d. 2+(3/v2) O e. 2+(2/v2)
The probability density function of a distribution is given by x f(x) = exp(-7). Use differentiation to show that the probability density function has a maximum at x = 0. The moment generating function of a distribution is M(t) = (q + pet)", where p € [0, 1], q = 1 - p and n is a positive integer. Use the moment generating function to find the mean and variance of the distribution in terms of p, q and n.
Show that the following are the probability density functions: fi(x) = e-*I(0,c0) (x) f2(x) = 2e¬*I(o,00) f(x) = (0 + 1)f1 (x) – Of2(x) 0 < 0 < 1