8. Hand in:Let Y1, Y2, ., Y,, be independent, uniformly distributed random variables on the interval [0, 0].Find thea probability distribution function of Y(m) = max(Y1, Y2, .... Y,).b density function of Y(m)-mean and variance of Y(m)-

Given that Let Y₁, Y2, ..., Y, be independent, uniformly distributed random variables on the…

Answered: 8. Hand in: Let Y1, Y2, ..., Y, be…

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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1)Let x and y be two continuous random variables whose function is the probability density joint is given by : a)Draw the relationship between the variables x and y on the Cartesian axes .b)Calculate the marginal pdfs px(X)and py(Y).c)Are the v.a.s x and y independent ?
Suppose the random variables X and Y have joint probability density function f(x,y) given by: (image)Find: P(X < Y) = fX|Y=y (x)
6.) Suppose X is continuously uniformly distributed on [−2, 2]. Let Y = X2. What is the density function of Y? What is the expected value of Y?
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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.)
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1) Let x be a uniform random variable in the interval (0, 1). Calculate the density function of probability of the random variable y where y = − ln x.
Let X ~ U[0,1] and Y = -βln(1-X). What is the distribution of Y? Justify.

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8. Hand in: Let Y1, Y2, ..., Y, be independent, uniformly distributed random variables on the interval [0, 0]. Find the a probability distribution function of Y») = max(Y1, Y2, .., Y„). b density function of Y(m)- c mean and variance of Y(m)- (п)