Suppose that X and Y have a discrete joint distribution for which the joint probability mass function is defined as follows: pX,Y(k,l)= c|k+l|, for k=1,0,1,and l=1,0,1; 0, otherwise. (a) Find c. (b) Find the marginal probability mass function pX(·) for X. (c) Compute P(|X - Y | less than or equal 0.9).

Suppose that X and Y have a discrete joint distribution for which the joint probability mass function is defined as follows: pX,Y(k,l)= c|k+l|, for k=1,0,1,and l=1,0,1; 0, otherwise. (a) Find c. (b) Find the marginal probability mass function pX(·) for X. (c) Compute P(|X - Y | less than or equal 0.9).

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: Suppose that the joint distribution of X and Y is uniform over the region in the xy-plane bounded by…

A: Please note that I have answered as per our guidelines. Please repost the remaining questions…

Q: Let X and Y be independent v.a with uniform distribution on the interval (0, 20) and (0, 30)…

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

Q: Is f(x) a legitimate probability mass function? (1 – p)"='p =p+ (1 – p)p + (1 – p)²p+ • …· ² 1 x=1

A: We know that to be a legitimate mass function we must have 0≤f(x)≤1 for all x. And the sum of all…

Q: The distribution function ‘F’ is given by F(x) = 0, x < 0 ½, 0 ≤ x <1 3/5, 1 ≤ x < 2 4/5, 2 ≤ x < 3…

Q: The Joint P.D.F. of X and Y is given by f(x,y)-(3-x-y (3-x-y.0<x<1, 0<y<1 0, otherwise a) Find…

Q: 6. Let T be a right triangle with vertices at (0,0), (0,4), and (3, 4). We pick a random point in T…

A: Given problem is :

Q: Let X has uniform distribution on [-1,1]. Find E(X|X²).

A: Given: X has uniform distribution on [-1,1]. Then the pdf is: f (x)=12for -1<X<10Otherwise

Q: Set n > 2. Let X1, X2, ..., Xn denote a random sample from a uniform distribution on (0, 1) i.e.…

A: Given that, Xi ~U(0, 1) i= 1,2,3......n We have to find E(R) where R=Y(n) - Y(1)

Q: Suppose you have the following random sample with n independent obser- vations: X1, X2, . üd…

Q: 3. Let X be a random variable with distribution function P(X ≤x} = { 0 x 1 if x ≤ 0, if 0 1. Let F…

Q: b) Suppose that X₁ and X₂ have the joint probability density function defined as f(x₁, x2) = {Wx₁x2₁…

A: Given that b) Suppose that X₁ and X₂ have the joint probability density function defined as We…

Q: Let X be a discrete random variable taking values {x1, x2, . . . , xn} with probability {p1, p2, . .…

A: Probability Mass Function :- If X is a One-dimensional discrete random variable taking at most a…

Q: Suppose that the probability density functions of x is 3x2, 0<x < 1) F(xE0, Elsewhere ) a) Determine…

A: Given that, P.d.f. is f(x)= 3x2, 0<X<1 C.d.f. of X is given by, F(x)= integration|0x f(x)dx

Q: Suppose that X has a continuous distribution with probability density function fx(x) = 2 * x on the…

A: Solution (b)

Q: 1 (a) ƒ (kx) = 2x+1_2²²₂ = - 2*, x = 1, 2, ..., N, and zero elsewhere (b) f(x)=p(1-p)*, x=0,1, 2,…

A: As per bartleby guidelines we can solve only first three subparts and rest can be reposted # To…

Q: Let R have probability mass function (pmf) p(r)=1/8 for r=1,2,...,8. Fin (1)the cumulative…

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

Q: a) Let X₁, X2, X3,..., X30 be a random sample of size 30 from a population distributed with the…

Q: Q.1 A contimuous random variable X has the following function -3 sxs 15 fx (x) = }K* 0; e.w. @For…

A: Given Information: Let X be a continuous random variable. fxx=1K -3≤x≤15 i) Determine the value of…

Q: Let X1,..., Xn be a random sample from a population with probability density function (pdf) f(x | 0)…

A: We have given that Let X 1 ,...,X n be a random sample from a population with probability density…

Q: A continuous random variable X has the probability density function f(x) so that f(x) is 0 for…

Q: i) Find the marginal distribution of X₁. ii) Find E(X₁X₂).

Q: i) the value of w that makes f(x₁, x₂) a probability density function. ii) the joint cumulative…

Q: a) The continuous random variable X has probability density function f(x) = 0(1 – x)º-1, 0 0 i) Find…

A: The probability density function is, fx=θ1-xθ-1

Q: Suppose that the probability density function of x is f(x) = 0, (3x², 0 (2/3)) b) Determine the…

Q: et X1,..., Xn be a random sample from a uniform distribution on the interval [20,0], where 0. et…

A: Solution

Q: If F(x) is the CDF of the standard normal distribution Z~Norm(0,1), show that (a) For 0 ≤ a < b,…

A: (a)From the given information, F(X) is the CDF of the standard normal distribution.

Q: b) Suppose that X₁ and X₂ have the joint probability density function defined as (WX1X2, f(x₁,x₂) =…

Q: b) Suppose that X₁ and X₂ have the joint probability density function defined as f(x1, x₂) =…

A: Given The joint pdf of X1 and X2: f(x1,x2) = wx1x2, 0 <x1< 1, 0 < x2 < 1

Q: Let X and Y be two continuous random variables with the joint probability distribution function:…

Q: Pind the values of the constants a' and 'b' such that the CDF Кx (х) %3D 1- а.е xb] и (х) is a valid…

Q: 3. Find the value of k for the probability mass function f(x) = k () ) for x = 0,1,2. %3D

A: We are given a probability mass function and we need to find k and cumulative probability…

Q: A random variable X has a Pareto distribution if and only if its probability density is for a > 1…

Q: Show that for any e > 0 and Sn = Show that a statistic S, in a) is the maximum likelihood estimator…

A: The given probability function is of Poisson distribution with parameter θ due to the form of given…

Q: If the random variable T is the time to failure of a commercial product and the values of its…

Question

Suppose that X and Y have a discrete joint distribution for which the joint probability mass function is defined as follows:

pX,Y(k,l)= c|k+l|, for k=1,0,1,and l=1,0,1; 0, otherwise.

(a) Find c.

(b) Find the marginal probability mass function pX(·) for X.

Video Video

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

Step 3

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 4 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

1. Let X have the probability density function f(x) = cx(1-2) for 0≤x≤ 1 and f(x) = 0 otherwise. (a) Show that c = 6. (b) Find the cumulative distribution function F(x) = P(X ≤ z). (c) Calculate P(.1 < X <5). (d) Find the mean, variance and standard deviation of X.
b) Let X₁, X2, X3,...,Xn be a random sample of n from population X distributed with the following probability density function: f(x;0)=√√2n0 0, -20₁ if -∞0 < x <∞0 otherwise (i) Find the parameter space of 0. (ii) Find the maximum likelihood estimator of 0. (iii) Check whether or not the estimator obtained in (ii) is unbiased. (iv) Find the Fisher information in this sample of size n about the parameter 0.
3. Let X; N iid U(0, 1) for i e {1, 2, ...,n}. (a) Compute the pdf of Y; = - log(X;), name the distribution that Y; follows and provide any parameter value or values needed. (b) Compute the pdf that W = [I", X, = X1 X2... X, follows. You may use the result given as part of the Example 2.6 video (even though it will only be proved in Chapter 3). (c) Compute E[W] in the two following ways: (i) through exploiting independence of the X, and using EUV] = E[U]E[V] for any independent random variables U and V. (ii) using the pdf of W computed in the previous part.
b) Let X₁, X2, X3.....Xn be a random sample of n from population X distributed with the following probability density function: ze zo, f(x;0)=√2m0 0, (i) Find the parameter space of 0. (ii) Find the maximum likelihood estimator of 0. if -∞
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.]
b) Suppose that X₁ and X₂ have the joint probability density function defined as f(x₁, x₂) = (x1x²,0x₁51, 0 ≤ x₂ ≤1 elsewhere Find: i) the value of w that makes f(x₁, x₂) a probability density function. ii) the joint cumulative distribution function for X₁ and X₂. iii) P (X₂ ≤ | X₂ ≤ ³).
Let X1,..., Xn be a random sample from a uniform distribution on the interval [20, 0], where 0 0. Let X(1) < X(2) <...< X(n) be the order statistics of X1, ..., Xn.
State the CLT for independent identically distributed real RVs with mean u and variance a². Suppose that X. X,. . . are independent identically distributed random variables each uniformly distributed over the interval [0, 1]. Calculate the mean and variance of In X. Suppose that 0
Suppose the joint distribution of the two random variables X1 and X2is given by S6x2, 0< x2 < x1 < 1, (o, f(x1, 22) = - elsewhere. (a) Find the marginal distribution fx, (x1) of X1 and verify that it is a valid density function. (b) What is the probability that X, is less than 0.5, given that X, is 0.7?
b) Suppose that X₁ and X₂ have the joint probability density function defined as ƒ(x1, x₂) = {W*1*2* (Wx₁x₂, 0≤x₁ ≤ 1, 0 ≤ x₂ ≤1 elsewhere Find: i) the value of w that makes f(x₁, x₂) a probability density function. ii) the joint cumulative distribution function for X₂ and X₂. iii) P (X₁ ≤ 1X₂ ≤²).
1. Verify whether the following functions can be considered as probability mass functions: (i) P(x = x) = x² + 1 18 (iii) P(X= x) = -, x = 0, 1, 2, 3 (ii) P(X - x) - ²-2, -, x= 1, 2, 3 2x + 1 18 -, x = 0, 1, 2, 3 [Ans.: Yes) [Ans.: No] [Ans.: No]
Let Y1, Y2,., Ya be a collection of independent random variables with distribution function y 8 Show that Y converges in probability to a constant, and provide that constant. 1