Q2)A fast-food restaurant operates both a drive-through facility and a walk-in facility. On a randomlyselected day, let X and Y, respectively, be the propor-tions of the time that the drive-through and walk-infacilities are in use, and suppose that the joint densityfunction of these random variables isf(x, y)=[(x+2y),10,0≤x≤ 1,0 ≤ y ≤ 1,elsewhere.(a) Find the marginal density of X.(b) Find the marginal density of Y.(c) Find the probability that the drive-through facilityis busy less than one-half of the time.

Let X and Y be two continuous random variables defined over the sample space S. Then the continuous…

Answered: A fast-food restaurant operates both a…

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

Consider two independent random variables X1 andX2 having the same Cauchy distributionf(x) = 1π(1 + x2)for − q < x < qFind the probability density of Y1 = X1 + X2 by usingTheorem 1 to determine the joint probability density ofX1 and Y1 and then integrating out x1. Also, identify thedistribution of Y1.
Suppose that X, Y , and Z are random variables with a joint density f(x, y, z) = ( 6/((1+x+y+z)^4)) , when x, y, z > 0, and 0, otherwise. Determine the distribution of X + Y + Z.
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),
Let X denote the reaction time, in seconds, to a certain stimulus and Y denote the temperature (◦F) at which a certain reaction starts to take place. Suppose that two random variables X and Y have the joint density
Let X1 and X2 be independent chi-square random variables with r1 and r2 degrees of freedom, respectively. Let Y1=(X1/r1)/(X2/r2) and Y2=X2. (a) Find the joint pdf of Y1 and Y2.
Let Xi be arandom sample from U(0,1)prove that Xn’ convarges in probability to 0.50
Let X and Y be two jointly Gaussian real random variables, each with zero mean,variance 1, and correlation coefficient ρ ∈ (0, 1). Let a, b ∈ R be such that a2 + b2 = 1, and defineW := aX + bY .a. Find values for a and b to maximize the variance of W . Hint: Use eigendecomposition.b. Does the optimal W (from part a) have a probability density function? If yes, derive it. Ifnot, explain why.
If X is a continuous random variable find the CDF and density of the function y = x/3
Let X1 and X2 be two continuous random variableshaving the joint probability density f(x1, x2) = 4x1x2 for 0 < x1 < 1, 0 < x2 < 10 elsewhereFind the joint probability density of Y1 = X21 and Y2 = X1X2.
For a continuous random variable X having p.d.f. f and c.d.f. F , 10 random observations are obtained as follows: 12, 15, 15, 15, 18, 18, 20, 23, 23, 26 Apply kernel density estimation method, using a uniform kernel with bandwidth h = 5, to estimate the following: (a) f(15) (b) F(20) Compare the result of part (b) with its empirical estimate.
Let the joint pdf for the continuous random variables X and Y be: f(x,y) = { 4xy; 0<x<1, 0<y<1 0; elsewhere } What is the joint CDF of X and Y?
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]?

SEE MORE QUESTIONS

Recommended textbooks for you

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

SEE MORE TEXTBOOKS