Selected correct option after simplifying for each part Let the random variables X and Y follow the joint pdf2ye¯xifx > 0, 0 < y < 1otherwise{Mark the statements below that are true for this joint pdf.fx.x (x, y)=0Select one or more:a. The marginal density of Y is fy(y) = 2y on (0,1).b. X and Y are independent.c. E[XY] = 0.d. The conditional density of Y given X = x is proportional to xe assuming x > 0.e. The joint cumulative distribution function (cdf) tends to infinity as y tends to infinity.Of. X and Y are dependent.

Let the random variables X and Y follow the joint pdf 2yex fx,y (x, y) = ifx > 0, 0 < y < 1 otherwise Mark the statements below that are true for this joint pdf. Select one or more: O a. The marginal density of Y is fy(y) = 2y on (0,1). b. c. E[XY] = 0. Od. The conditional density of Y given X = x is proportional to xe¯* assuming x > 0. Oe. The joint cumulative distribution function (cdf) tends to infinity as y tends to infinity. O f. X and Y are dependent. X and Y are independent.

Let the random variables X and Y follow the joint pdf 2yex fx,y (x, y) = ifx > 0, 0 < y < 1 otherwise Mark the statements below that are true for this joint pdf. Select one or more: O a. The marginal density of Y is fy(y) = 2y on (0,1). b. c. E[XY] = 0. Od. The conditional density of Y given X = x is proportional to xe¯* assuming x > 0. Oe. The joint cumulative distribution function (cdf) tends to infinity as y tends to infinity. O f. X and Y are dependent. X and Y are independent.

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

Similar questions

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
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]?
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
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 (d) fZ|XY (z|x,y), (e) fX|YZ(x|y, z).
Suppose that the random variables X,Y, and Z have the joint probability density function f(x,y,z) = 8xyz for 0<x<1, 0<y<1, and 0<z<1. Determine P(X<0.7).
Given the random variables X and Y having the following joint density: f(x, y) = 2(x + y) for 0 < y < x < 1. A) Compute the conditional pdfs: fX│Y (x) and fY│X (y). B) Are X and Y independent?
Let f(x, y) = C/8, 0 ≤ y ≤ 4, y ≤ x ≤ y + 2, be the joint pdf of X and Ya) Find the value of C so that f(x,y) is a valid joint p.d.fb) Find the marginal probability density function of X, fX(x)c) Compute μX , μY , Cov(X, Y), and ρ.
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 Find the constant c, P(Y≥1/2), P(X < 2, Y >1/2), P(X < 1), Determine whether X and Y are independent.
Suppose that the random variables X and Y have a joint density function given by: f(x,y) = {c(2x+y) for 2≤x≤6 and 0≤y≤5, 0 otherwise P(3 < X < 5, Y >1), P(X < 3), P(X +Y > 5), Find the joint distribution function (cdf),
Assuming X and Y have joint density f(x; y) = 1/4 for all 0<=x<=2 and 0<=y<=2, and f(x, y) = 0 otherwise.(i) Show that X and Y are independent random variables, and each has the uniform distribution on [0; 2]?(ii) what is E(X) and Var(X)?(iii) Compute Var(X + Y ) and Cov(X + Y, Y )?
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 current in a certain circuit as measured by an ammeter is a continuous random variable X with the following density function, f(x) = 0.05x + 0.3 if 3 <= x <= 5, and 0 otherwise. (a) Calculate P(X ≤ 4). (b) Calculate P(3.5 ≤ X ≤ 4.5). (c) Calculate P(4.5 < X).