Please write each step. Given that X and Y are independent random variables with density functions.S2e-2 x >0fx(x) =x < 0| 4ye¬2y y > 0= (f) AfyY < 0Find the density function of X + Y.

Given, x+y is the independent variable fx(x)=2e-2xx≥00x<0fy(y)=4ye-2yy≥00y<0

Answered: Given that X and Y are independent…

Given that X and Y are independent random variables with density functions. | 2e-2z x > 0 fx(x) = x < 0 fy (y) = | 4ye-2y y > 0 y < 0 Find the density function of X + Y .

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: X is continuous random variable with probability density function px +1,0 k) =

A: (a) Here, Hence the value of p is -1. Since we can calculate q as follows: Hence the value of…

Q: A continuous random variable X that can assume any value between X = 2 and X = 5 has a density…

Q: If the independent random variables X and Y have the marginal densities f(x) = ⎧ ⎪⎪⎨ ⎪⎪⎩ 1 2 for 0…

A: From the given information, it is clear that, fx=12 0<x<20 elsewhereπx=13…

Q: If the probability density of X is given by f(x)= 6x(1–x) 0<x<1 Find the probability density…

A: We know, For any given density function. ∫-∞∞fx dx =1 Therefore, ∫016x1-x dx = 1 Let y…

Q: For random variables X and Y with the following joint density function: f (x, y) = (xy+ 2), 0 < x <…

A: The given joint density function of X and Y is as follows:

Q: Joint density functions of two random variables is given by fxx (x, y) = 18y² x³ Find (a) E[X], (b)…

Q: If p(x, y) is the joint probability density function of randomvariables X and Y, what does the…

A: Probability density function p(x, y) is given.

Q: Given the probability density function of X : -1sxs0 2 S« (x)=< x20 a. Find the probability density…

A: a) The given function is fX(x) = 12-1≤x≤012e-xx≥0 The probability density of Y = X2 is as follows:…

Q: 2. If X and Y are two random variables, having joint density function 1 -(6-x-y) 0≤x≤ 2, 0≤ y ≤ 4 24…

A: According to our guidelines we can solve only first three sub-parts. For remaining sub-parts please…

Q: The joint density function of random variables X and Y is given by f(x, y) = {12xy(1 – x) 0 < x, y <…

A: Given : f(x,y) = 12xy(1-x) ; 0<x<1 ,0<y<10 ; otherwise…

Q: The random variables X and Y have a joint density function given by S2e-2. f(x.y) = 0<x< 00, 0<y<x…

Q: Suppose that X and Y are random variables with joint density function fxy (a, y) = 8xy for 0<y< x <…

A: We have given joint density function fX,Y(x, y) = 8xy for 0<y<x<1(and fX,Y(x,y) =0…

Q: Suppose X and Y are random variables with joint density function. S0.1e-(0.5x + 0.2y) if x > 0, y >…

A: a) Given function represents the joint density for X and Y. Hence, the correct option is YEs. b)…

Q: A random variable X has the density function: fx (x) = { 3 (3-x) 1<x<3 10 otherwise

A: Consider, EX2=∫xx2fxdx =∫01x2*65x2dx+∫133103-xx2dx =65x5501+3103x33-x4413…

Q: A random variable x has a density function f(x) = c(x+1) where 0 < x < 2| 2

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: 9. Let Y1, Y2,., Yn denote a random sample from the probability density function given by 0-1 0<y<3…

A: Solution:- Given that pdf of y f(yθ) = θ yθ-13θ , 0 ≤y≤30 , elsewhere

Q: A random variable X has the density function fx (x) for x 2 0 for x <0 Find E le2x/31

A: The random variable X has the density function, fx(x) = fx(x) = e-x, for x ≥00, x < 0

Q: Given that X and Y are independent random variables with density functions. 2e-2z x > 0 fx(x) = x 0…

A: The density function of X is fxx=2e-2x, x≥00, x<0. The density function of Y is…

Q: A continuous random variable X that can assume values between x = 0 and x = 4 has a density function…

Q: A continuous random variable X that can assume values between x=2 and x= 5 has a density function…

Q: The joint probability density of X and Y is given by 1 fx.y (x, y) = - +5xy; 0<x < 1; 0 < y < 2 3xy;…

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: Let f(x, y) = where C is a constant. (x² + 1)(y² + 1)’ Suppose that X and Y are random variables…

Q: The joint probability density of X and Y is given by 1 fx.y (x, y) +5xy; 0<x < 1; 0 < ys 2 0; e.w.…

A: Solution: The joint probability density function of X and Y is fX,Y(x,y)=x2+13xy; 0≤x≤1;…

Q: Let X and Y be continuous random variables with joint p.d.f. f(x,y) = {* (12x for 0< y< 2x < 1…

A: Given, Let X and Y be continuous random variables with joint pdf f(x, y)={ 12x; 0<y<2x<1 0;…

Q: Let Y1,...,Yn constitute a random sample from the probability density function given by T(20) fy…

A: Given that fy(θ)=τ(2θ)[τ(θ)]2yθ-1(1-y)θ-1 , for y∈[0,1]

Q: Q3- If the density function of X is (2x (x) = 0 < x < 3 %3D 0. w Find the probability mass function…

Q: Let X denote the reaction time, in seconds, to a certain stimulus and Y denote the temperature (°F)…

Q: The joint density function of X and Y is 1 fxy (x, y) ={100 0 <x< 5, 0<y<20 elsewhere Find the…

Q: Let X, Y be random variables, suppose X is N(0, 1) and Y = e2X. a) Obtain the density function of…

A: Solution

Q: Suppose that the random variables a and Y have the joint density function given by: f(x, y) = b(4x +…

Q: let X and Y have the joint density e-(x+y) for 0<x,y<∞ f(x.y)= other wise then X and Y are…

A: Solution: From the given information, the joint density function of X and Y is

Q: Suppose you have two independent random variables X ~ Exponential(A1) and Y Exponential(A2), d1 > 0,…

Q: pose that X and Y are random variables with the joint density function cx2 0 2).

A: Solution

Q: X is a continuous random variable and its density function is S kz Oszs1, {1525 0) = What is k? Oa2…

A: Random variables are of 2 types, discrete and continuous. A discrete random variable can only take…

Q: At a restaurant, the density function for the time a customer has to wait before being seated is…

Q: and satisfy 0<0, <0, < T. Find and sketch the probability density function of the transferred random…

Q: Suppose you have two independent random variables X ~ Exponential(A1) and Y Exponential(A2), A1 > 0,…

A: X~Expλ1Y~Expλ2 Here, λ1>0 and λ2>0 It is given that X and Y are independent exponential…

Q: Let X and Y be two continuous random variables such that the joint density function is given by: 3…

Q: Let X and Y be two random variables with joint density function 2, 0 <x < y < 1, fx,y (x, y) = 0,…

A: First we need to find the conditional values then calculate the expectations and variances, EYX=x…

Q: Let X and Y be continuous random variables with joint p.d.f. f(x, y) = {12x for 0<y<2x<1 elsewhere…

A: Solution: The joint pdf of X and Y is

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

A: The joint probability function of X, Y is given as f(x,y)= 3x-y9 1≤x≤4…

Q: Consider the random variables X and Y with joint probability function f (x.y) specified below: x 2…

A: Note: " Since you have posted many sub-parts. we will solve the first three sub-parts for you. To…

Q: Suppose that the random variables X and Y have a joint density function given by: f(x,y)={cxy for…

Q: Let Y1,..., Yn constitute a random sample from the probability density function given by 2 fy (v0) =…

A: Given, For the pdf of random samples Y1, Y2 , ..., Yn fYy|θ=2θ2θ-y ,y∈[0,θ] Let, sample mean be y¯

Q: The two random variables and Y have the joint density function: с, f(x,y)= c, 0<2y <x; 0<x<1,

A: From the given information, the joint density function for X and Y is, The constant c value is…

Q: - If the density function of X is (2x (x) = } 9 0 < x < 3 0. w Find the probability mass function of…

A: Given that Y=X [floor function]This means Y=0 when 0≤X<11 when 1≤X<22 when 2≤X<3So…

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

Please write each step.

Given that X and Y are independent random variables with density functions.
S2e-2 x >0
fx(x) =
x < 0
| 4ye¬2y y > 0
= (f) Af
yY < 0
Find the density function of X + Y.

Expert Solution

This question has been solved!

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

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Equations$

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 random variables X and Y have the following joint probability density function:f(x,y)={e−x−y , 0<x<∞; 0, elsewhere. What is Cov(X,Y)(X,Y)?
Let X be a random variable with density function f(x) = cx−3, if x ≥ 1, 0 otherwise. a) Find c.b) Find P (3 < X ≤ 6).c) What is P(X = 3)?
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)?
Suppose that the random variables X and Y have a joint density function given by: f(x,y)={cxy for 0≤x≤2 and 0≤y≤x, 0 otherwise c=1/2 P(X < 1), Determine whether X and Y are independent
Suppose that two continuous random variables X and Y have joint probability density function fxy = A( ex+y + e2x+y) , 1 ≤ x ≤ 2 ,0≤ y≤3 0 elsewhere a. P ( 3/2 ≤ X ≤ 2, 1 ≤ Y ≤ 2) b. Are the random variables X and Y independent? c. find the conditional density X given Y = 0
For a certain psychiatric clinic suppose that the random variable X represents the total time (in minutes) that a typical patient spends in this clinic during a typical visit (where this total time is the sum of the waiting time and the treatment time), and that the random variable Y represents the waiting time (in minutes) that a typical patient spends in the waiting room before starting treatment with a psychiatrist. Further, suppose that X and Y can be assumed to follow the bivariate density function fXY(x,y)=λ2e−λx, 0<y<x, where λ > 0 is a known parameter value. (a) Find the marginal density fX(x) for the total amount of time spent at the clinic. (b) Find the conditional density for waiting time, given the total time. (c) Find P (Y > 20 | X = x), the probability a patient waits more than 20 minutes if their total clinic visit is x minutes. (Hint: you will need to consider two cases, if x < 20 and if x ≥ 20.)
The proportion of people who respond to a certain mail-order solicitation is a random variable X having the following density function. f(x) = 2(x+1)/3, 0<x<1, 0, elsewhere Find σ2g(X) for the function g(X)=5X2+4. σ2g(X)= ?
Let X and Y be a pair of continuous random variables with a joint density fx,y(x,y). Assume that fx,y(x,y) = cxy for x greater than or equal to 0, y greater than or equal to 0, and x + y less than or equal to 1. Here c is a constant. Assume that fx,y(x,y) is 0 elsewhere. What is the constant c equal to? With the value of c, what is E[XY]?
The PDF of a continuous random variable X is as follows: f(X)= c(4x2 - 2x2) 0<* x <* 2 (*less or equal to) a. For this to be a proper density function, what must be the value of c ?
2. Identify the probability density function, then find the mean and variance without integrating. b. f(x) =1/6 e^−x/6, [0,∞) c. f(x) =1 / 3√2π e^−(x−16)^2/18, (−∞,∞)
b) Given the following density function of the random variable X: f(x) = (1+x)2, 0<x<1 = 0, Find E(X) and V(X).
Consider the random variable X with PDFf(x) = e−x / (1 + e−x)2 , x ∈ R.Find the density function of Y = 1/ (1 + e−X)