A service facility operates with two service lines. The random variables X and Y are the proportions of the time that line 1 and line 2 are in use, respectively. The jointprobability density function for (X,Y) is given below. Complete parts (a) through (d) below.f(x,y) = x+y², 0≤x,y≤ 1,f*0,elsewhereE(XY) =(Simplify your answer.)C(a) Determine whether or not X and Y are independent.X and Yindependent, since f(x,y)equal towhere g(x) and h(y) are the(b) It is of interest to know something about the proportion of Z=X+Y, the sum of the two proportions. Find E(X+Y). Also find E(XY).E(X+Y)=(Simplify your answer.)of X and Y, respectively.

The joint pdf of X and Y is f(x,y)=94x2+34y20≤x,y≤10elsewhere

Answered: A service facility operates with two…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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.)
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 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),
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
The random variables X and Y have the joint density: fX,Y(x,y) = 2−x−y, for 0<x<1, 0<y<1 0, otherwise For each of the following, please provide your answers in three decimal places: (a) What is the expected value of X? (b) What is the variance of X? (c) What is the covariance of X and Y? (d) What is the correlation of X and Y?
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)?
If the joint probability density of X and Y is given byf(x, y) = 24y(1 − x − y) for x > 0, y > 0, x + y < 10 elsewhere find(a) the marginal density of X;(b) the marginal density of Y.Also determine whether the two random variables areindependent.
A continuous random variable X has density given by: f(x)= {1/2, -0.5≤x<0.5 {1, 0.5≤x≤1 {0 Based on this information, answer each alternative. a. P(X< −0.39 or X≥0.74): b. P(X≥−0.01): c. P(0.34≤X≤0.79): d. P(X≥0.36|X≤0.99): e. P(X≤0.63|X≥0.31):
Given the density function of the random variables (X,Y) as f(x,y)=3x2y+ 3xy2 , for 0 ≤ x ≤ 1 , 0 ≤ y ≤ 1 = 0 otherwise Find the marginal and conditional density functions. Also find the conditional probability P [1/2 ≤ x ≤ 3/4 | 1/2 ≤ Y ≤ 2/3]
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.
Let X and Y be two independent random variables with densities fX(x) = e^(-x), for x>0 and fY(y) = e^y, for y<0, respectively. Determine the density of X+Y.
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?

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