9.Two discrete random variables X and Y have joint probability mass function(pmf)f(x) =k x = 1,2,n(n+1)otherwise{=01,2,...,n; y = 1,2, x.·(d)Use the fact that E(Y) = Ex (Ey\x(Y|X)), where Ex( ) and Ey|x ( ) are theexpected values with respect to X and with respect to Y given X, respectively,n(n+3)to show that E(Y)4

To find the expected value of Y, E(Y), using the law of total expectation, we can break it down as…

Two discrete random variables X and Y have joint probability mass function (pmf) ‚n;_y=1,2, x. f(x) = بر k x = 1, 2, n(n+1) 0 otherwise (d) Use the fact that E(Y) = Ex (Ey|x (YX)), where Ex() and Exx() are the expected values with respect to X and with respect to Y given X, respectively, n(n+3) to show that E(Y) 4 =

Two discrete random variables X and Y have joint probability mass function (pmf) ‚n;_y=1,2, x. f(x) = بر k x = 1, 2, n(n+1) 0 otherwise (d) Use the fact that E(Y) = Ex (Ey|x (YX)), where Ex() and Exx() are the expected values with respect to X and with respect to Y given X, respectively, n(n+3) to show that E(Y) 4 =

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: True or False; For a continuous random variable X, P(X=x) = f(x) 1. True 2.False

A: In statistics, the continuous variables are variables whose values can be given by an interval, they…

Q: 1 V(X) for i) X ~ U{1,n}, ii) X~ Geometric (p), iii) X P

A: We have given that X be a random variable which follows 1) Uniform distribution, i.e. X∼U{1,n}2)…

Q: 2. Let X be a random variable with density function f(x) = = √ (2x3 -8x2 +5x+6), 1<x<2, 0, elsewhere…

A: given function is f(x)=

Q: Let X and Y be independent and identical exponential random variables with parameter 0. Showthat Z =…

A: and represent independent and identical exponential random variables.The parameterIt must be shown…

Q: X2 are independent continuous random variables with a uniform distribution in the interval (a, b).…

Q: The weekly demand for propane gas (in 100's of gallons) from a particular facility is a random…

Q: Let X and Y be two continuous random variables having joint pdf fX,Y (x, y) = (1 + XY)/4 , −1 ≤x ≤1,…

A: Given that, X and Y are two continuous random variables. The joint pdf of X and Y is given as:…

Q: Problem 5.2 The continuous random variables X and Y have joint PDF fx,x(x, y) = { cr*y, -1<r<1, 0< y…

A: "Since you have posted a question with multiple subparts, we will solve the first 3 sub-parts for…

Q: The probability distribution for the random varaibles X and Y is shown in the table below. Find the…

A: Give data: 0 1 2 P(Y) 0 11/73 18/73 14/73 43/73 1 10/73 8/73 0 18/73 2 12/73 0 0 12/73…

Q: let x be a random variable with moment generating function Mx(t)=(0.6 + 0.4e^t)^20 then the variance…

Q: The density of a random variable X is f(x) = C/x^2 when x ≥ 10 and 0 otherwise. Find P(X > 20).

A: Given:fx=cx2, x≥10…

Q: Prove that f_x is a true probability function, find its expected value and its variance

A: HERE FOR VALID PROBABILITY DISTRIBUTION FUNCTION TOTAL PROBABILITY IS ALWAYS EQUAL TO 1

Q: For the continuous probability functionf(x) = Kx when x20 find

Q: (Y-1)². Use one decimal place accuracy.

A: Given that Y ~ Uniform (1 , 11)

Q: Let X,Y be two random variables and take values in {0,1} and whose joint distribution is given by: (…

A: First, we need to calculate the expected values of X, Y, X^2, and Y^2. The expected value of a…

Q: A random variable Y has a uniform distribution over the interval (8,, e,). Derive the variance of Y.…

Q: The continuous random variable XX has a probability density function (pdf) given by Part(d) Find…

Q: Let X1, X2, ..., Xn be a random sample from a Uniform(0,0 + 1) population with 0 > 0, *(3)**(3+1) X…

A: Given that, Let X1,X2,...,Xnbe a random sample from a uniform θ,θ+1population with θ>0 where n is…

Q: If the joint Pdf of two random variables X and Y is fry (x, y) = 24y (1 - x) for 0 sy<r<1, find the…

Q: Let joint Probability distribution function of random variables X and Y be (1/3 if (x, y) = (1, 1)…

A: The joint probability distribution function for X and Y is, P(x,y)=13, if(x,y)=(1,1)13, if…

Q: A continuous random variable X has pdf f(x) = (x^3)/4 0 < x < 2 0…

A: Given , A continuous random variable X has pdf f(x) = x34,0 < x < 2 0,Otherwise

Q: For a fully continuous 20-payment whole life insurance policy of 1,000 on (40), you are given: x (i)…

A: Given,The annual premiumInsurance type: 20-payment whole life insurance policy of 1000Age : 40

Q: À continuous random variableX has a probability density function (p.d.f) given by f(X)=K(10-X)(X-40)…

Q: (i) Determine the value ofk (ii) Let a = -1 and b = 2.

Q: Two discrete random variables X and Y have joint probability mass function pmf) ) J 0 f(x) = Show…

Q: For the continuous probability function f(x) = Kx² e¯× when x ≥ 0 find i) k ii) mean iii) variance

Q: A 5 The random variable X has the geometric distribution with probability mass function (pmf) Px(x)…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: (1) Let X = b(16, find E(4-3x) and distribution function.

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: sider the function f (x) = (1/24(x^2 +1) 1 < or = x < or = 4) = (0 otherwise)…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Suppose X is a random variable whose pdf is given by f(x) =k(4x-2x^2) 01)

Q: A variable X has a probability function f(x, 0) = 0e 0x; x≥0 y >0. The parameter 0 is estimated…

A: The given probability distribution of random variable X is exponential distribution.So in that…

Q: The manager of a bakery knows that the number of chocolate cakes he can sell on any given day is a…

A: Answer: Given, The probability mas function is; 0 1 2 3 4 5 1/12 1/12 3/12 4/12 2/12 1/12…

Q: Let X~ N(0,0²) and Y~ N(0, ²) be independent random variables and Z = X + Y. (a) Find the LMMSE…

A: In this problem, we are given two independent random variables, X and Y, which follow normal…

Question

9.
Two discrete random variables X and Y have joint probability mass function
(pmf)
f(x) =
k x = 1,2,
n(n+1)
otherwise
{
=
0
1,2,...,n; y = 1,2, x.
·
(d)
Use the fact that E(Y) = Ex (Ey\x(Y|X)), where Ex( ) and Ey|x ( ) are the
expected values with respect to X and with respect to Y given X, respectively,
n(n+3)
to show that E(Y)
4

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: Determine expression for k

VIEW

Step 2: Calculate E[Y]

VIEW

Solution

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Follow-up Questions

Read through expert solutions to related follow-up questions below.

Follow-up Question

Hi!

I don't understand how 4(n+1)/(n-1) matches n(n+3)/4.

They are not equal as far as I can see or understand. Is there an error in the solution or am I missing something?

Brgds

Solution

by Bartleby Expert

SEE SOLUTION

Similar questions

Q4) If X is a continuous random variable having pdf ke~ (2x+3y) x>0y>0 xy) = = e p(x) { 0 otherwise Find a) the constant k b) P(X>1) ¢) X, X2, 02, standard deviation.
3. Let X and Y be continuous random variables with joint PDF (3x 0s ysxs1 f(x, y) = {* otherwise Determine the correlation of variables X and Y.
Let X be a continuous random variable whose moment generating function is 4x(t) = (5) ³. Find Var (X)
For the continuous probability function f(x) = Kx² ex when x ≥ 0 find i) k ii) mean iii) variance =(A=X) q
(47) Let X z b(8,-) find E(5+6x) and distribution function.
2- Let the probability density function of the random variable X is - {²()* Then My(t) is (a) 2(3-e¹)-1 (c) 2e¹(3-e¹)-1 f(x) = ‚x = 1,2,3, ... 0 , otherwise (b) 3(2 – e¹)-¹ (d) e' (3-e¹)-1 a O
Two discrete random variables X and Y have joint probability mass function (pmf) (a) (b) (c) ƒ(x) = { 5 0 Calculate the value of k. Show that f(x|y) Show that f(y x) = k n(n+1) = 1 n 1 8 x = 1,2,..., n; y=1,2,...,x. otherwise
Prove this
Suppose that the random variables X, Y, Z have multivariate PDFfXYZ(x, y, z) = (x + y)e−z for 0 < x < 1, 0 < y < 1, and z > 0. Find (a) fXY(x, y), (b) fYZ(y, z), (c) fZ(z)
1 Ex//let xa random variable with pm f p X=xN N= N , x=1,2,.., N and let Y=a+bx where a, beR find Ey and Var(x)
9 Let the probability density of the two-dimensional random variable (ξ, η) be (4e**, x > 0; f;(x)=• (0, 6e", y>0; -6y f,(v) =; 0, x<0. y<0. Find E(2 { +3 n ).
B) Let X and Y be discrete random variables with joint probability function 2-y+1 9 for x = 1,2 and y = 1, 2 p(x, y) otherwise Calculate E(Y/X).