Q2/B/ Two random variables X and Y with joint density function given by: f (x, y) = 3 (2x + 4y) 0S x, y <1 %3D elsewhere (a) Find the marginal density of Y. (b) Find the marginal density of X. (c) Find P(x < 1/3)

Q2/B/ Two random variables X and Y with joint density function given by: f (x, y) = 3 (2x + 4y) 0S x, y <1 %3D elsewhere (a) Find the marginal density of Y. (b) Find the marginal density of X. (c) Find P(x < 1/3)

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: Q2/B/ Two random variables X and Y with joint density function given by: -(2x + 4y) 0 < x, y < 1…

Q: Q2. Here, the joint density function of two random variable X and Y are, (x,y) = {cCx*y* c(x*y²…

Q: The random variable X has the Cauchy density f(x) = 1/π(1+x2) for −∞ < x < ∞. Find the probability…

Q: The joint density function of X and Y is given by f(x, y) = 2x + 2y,0 < x < y Find the marginal…

A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts. In case…

Q: ata Y are independent random variables with density functions Jx (x) = e* . u (x) and fy (y) = 2 -…

Q: a) A continuous random variable Y has density function 3-2y f(y)={3 e „y > 0 ,elsewhere Find the…

Q: The random variables X and Y are related as Y= X. Find the density function of voriable Y.

Q: f(x) = { 3 sin(x) 0 < x < n, otherwise multiplier to convert f(x) into a probability density…

A: Given f(x) and we need to find multiplier that makes it a pdf and also find its expected value if…

Q: Consider two continuous random variables X and Y with marginal distributions g(x) and…

Q: Example 15: Let X and Y be continuous random variables with a joint density function f (x, y) = e, 0…

A: Answer: From the given data

Q: 1. X and Y are independent exponentially distributed random variables with the parameter 1. Find the…

Q: 1. Consider the random variable X and Y with joint density function x+y f(x, y) = (*0," 0Sx,y 0.5,…

A: 1. The density function is given as- fx,y=x+y, 0≤x,y≤1 0, elsewhere Marginal…

Q: (1) Find marginal density of X. (2) Find conditional density of Y on X (3) Find P(2 <Y <3lx = 1).

A: The joint density function of X and Y is givne by, = 0 ; otherwise Our aim is to find the…

Q: Consider the random variables with X and Y with joint density function given by ky when 0 <y < 2x <…

A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts. In case…

Q: Two non-negative random variables X and Y have a joint density function f(x, y) = r'e-v *1) x> 0, y…

Q: Let Y1 and Y2 be continuous random variables with joint density function given by fy Y2) = 0 < y2…

A: Part a: If f(y1,y2) is a probability density function then…

Q: 4. Let X and Y be random variables. The density function of X is 1 | 24x²;0 < x <: 2 ; f (x) = - 0;…

Q: 2. The joint density function of the random variables X and Y is given by $8xy 0<x<1 , 0<y<x f(x,y)…

A: We have been given the joint density function of random variables X and Y as, f(x,y)=8xy 0≤x≤1,…

Q: (a) Give the marginal density of X1. (b) Give the marginal density of X2. (c) Give the conditional…

Q: DETAILED SOLUTION NEEDED

A: Joint Density Function

Q: onsider continuous random variables X and Y with the joint probabi on (PDF): cxy, if 0≤x, y ≤ 2,…

Q: 3.63 Two electronic components of a missile system work in harmony for the success of the total…

A: Solution

Q: The joint probability density function of two dimensional random variable(X,Y) is given 8. xy,…

Q: 1. Find the density of Y = 1- e-ax when X ~ Exp(X). Note that the density of X is if r > 0, ,…

Q: A continuous random variable has a density function f(x)= 2(5-x)/5 , where 2<x<3. Calculate the…

A: Graph:

Q: 3 4x 0 <x, <1, Let X, have the density function f,(x,)= If the conditional 0, otherwise.…

A: From the given information, the density function for X1 is, Given that the conditional distribution…

Q: 4. Let X and Y be independent random variables with the Cauchy density 1 f(x) = T(1+ x2) - O < x <∞.…

A: * x and y are independent Cauchy distribution then to find joint pdf of u=2x-y & v=x+y

Q: The joint probability function of random variables X and Y is given to be: Зх — у 1<x< 4,1 < y <2…

A: The marginal density function of random variable X is computed by integrating the joint probability…

Q: The joint probability function of random variables X and Y is given to be: ( 3x – y f(x, y) =…

A: Given: The joint probability function of random variables X and Y is:…

Q: A fast-food restaurant operates both a drive- through facility and a walk-in facility. On a randomly…

A: Let X and Y be two continuous random variables defined over the sample space S. Then the continuous…

Q: 2. Let X denote the reaction time, in seconds, to a certain stimulus and Y denote the temperature…

A: c. Consider the joint density function, fx,y=1.5x2+y20≤x,y≤10elsewhere To find the marginal density…

Q: The joint probability function of random variables X and Y is given to be: 3x - y 1<x< 4,1 < y <2…

A: The marginal density function of x…

Q: et x and y have joint density function f(x,y) = 2e ^-x-y 0<x<y<∞ are they independent? find the…

A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts. In case…

Q: Example. Suppose the joint density of (X,Y) is Find the marginal pdf of X and Y. f(x,y) =…

A: It is given that the joint probability density function of X and Y is, f(x,y) = e-(x+y),…

Q: 2. Let X be a Gamma random variable with parameters A and k E N; i.e., X has density 入kek-le- (k-1)!…

A: GivenXk be a gamma random variable with parameters λ and k, Y be an exponential random variable…

Q: Example. Suppose the joint density of (X,Y) is Find the marginal pdf of X and Y. f(x, y) = 2,0 ≤ x,…

A: Given,f(x,y)=2 ; 0≤x,y≤1 , 0≤x+y≤1

Q: Let X and Y continuous random variable with joint density function f(x, y) = { (2-x−y) for 0 < x, y…

A: Given information: fx,y=342-x-y, 0<x, y<2, 0<x+y<2

Q: Consider two continuous random variables X and Y with marginal distributions g(x) and…

A: Given,

Q: A random variable X has a density function f(x) = cx² 1 x2) 3. P(1/2 <X <3/2)

Q: b) Let X and Y be jointly continuous random variables with the following joint density function |…

A: Dear student, As per the guidelines, I can solve only the first three subparts. Kindly repost the…

Q: Suppose that X and Y are continuous random variables with joint pdf given by c(x²+y?) 0<x<1, 0<y<1…

A: We want to find the value of C and Marginal density of y and E(y) Note: According to bartleby…

Q: Find the joint probability density of = x + Y, Zz X+Y Find the marginal pdf of Z2.

A: It is an important part of statistics. It is widely used.

Q: Suppose that X and Y have joint density given by: f (x, y) = 15x²y, 0 < x < y < 1. (a) Find the…

Q: A random variable Y have a distribution with parameter a > 0 and yo > 0 if its density function is…

A: Solution

Q: X (f) = Ag cos ogi+Bo - sin wn t, where og is a real constant. Find the power %3D density spectrum…

Q: 3. Set up, but do not evaluate, an integral that will yield the density of Z = X + Y, where X is an…

Q: Suppose that X and Y have joint density given by: f (x, y) = 15x²y, 0 < x < y < 1. (a) Find the…

A: As per our guidelines we are supposed to answer only 3 sub-parts of any question so I am solving…

Q: 4. Let X and Y be continuous random variables with joint pdf (6-x-y) 0<x< 2, 2 < y< 4 f(x, y) ={8…

Q: Y has a density function (2 – y), 0 < y < 2 fV) = 0, elsewhere Find the mean and variance of Y.

A: See the hand written solution

Question

Q2/B/ Two random variables X and Y with joint density function given by:
(2x +4y)
0<x, y <1
f (x, y) =
elsewhere
(a) Find the marginal density of Y.
(b) Find the marginal density of X.
(c) Find P(x < 1/3)

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

Step 2

VIEW

Step 3

VIEW

Step by step

Solved in 3 steps

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

6.) Suppose X is continuously uniformly distributed on [−2, 2]. Let Y = X2. What is the density function of Y? What is the expected value of Y?
Let X and Y be random variables with the joint density function f(x,y)=x+y, if x,y element of [0,1], and f(x,y)=0,elsewhere. Find the expected value of the random variable Z = 10X+14Y.
Suppose a continuous random variable X~Fx(x): f(x,y) = {1/4e^-1x/4, if x≥0 0, x<0} What is the cumulative density function of Y=min{2,X}?
Let x be a continuous random variable with the density function: f(x) = 3e-3x when x>0 and 0 else Find the variance of the random variable x.
Consider two random variables X and Y whose joint probability density function is given byf_X,Y (x, y) = c if x + y ≤ 1, x ≤ 1, and y ≤ 1,0 otherwise What is the value of c?
If two random variables X1 and X2 have the joint density function given by f (x1, x2) = x1x2, 0 < x1 < 1, 0 < x2 < 2 0, otherwise Find the probability that (a) Both random variables will take on values less than 1 (b) The sum of the values taken on by the two random variables will be less than 1.
Suppose that the random variable B has the standard normal density. What is the conditional probability density function of the sum of the two roots of the quadratic equation x2 + 2Bx + 1 = 0 given that the two roots are real? KINDLY REQUEST YOU TO PROVIDE ME WITH COMPLETE SOLUTION
1) Let x be a uniform random variable in the interval (0, 1). Calculate the density function of probability of the random variable y where y = − ln x.
Let X and Y be two random variables with joint density function f(x,y) = (3 − x + 2y) / 60, for 1 < x < 3, 0 < y < 5. Is P(X > 2, Y < 3) equal to P(X > 2) × P(Y < 3)?
Consider two random variables X and Y whose joint probability density function is given byf_X,Y (x, y) = c if x + y ≥ 1, x ≤ 1, and y ≤ 1,0 otherwise What is the value of c? State the limits of integration for both x and y. f_X,Y (x, y) = c if x + y <=2 1, x ≤ 2, and y ≤ 2,0 otherwise What is the value of c? State the limits of integration for both x and y.
Suppose X and Y are independent and identically distributed (i.i.d.) randomvariables, each with the uniform distribution on [0, 1]. What is the cumulative distributionfunction and the density function of XY ?
The joint density function of the random variables X and Y is