Determine the marginal pdf of X, fx(x).Give the conditional density of Y, given X = Xo, fy\x(y|xo).3.6 From the marginal pdf of X, fx (x), in #3.1, give the cumulative distribution function of X, Fx (x).3.7 Find the following:(a) P[X > 1.2] from the cdf of X in #3.6(b) P[ Y < ½ | X = 1] (refer to #3.3)(c) E[ Y|X = 1](refer to #3.3) 3. Let X and Y be continuous random variables with joint probability density function= {3(x + y), if 0

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Answered: 3.6 From the marginal pdf of X, fx (x),…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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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.)
a. What is the joint marginal PDF of X and Z?b. What is [P 0 <= Y <= 3/2 | X = 1/3 Z = 5/2]?
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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
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Suppose that we want to estimate the parameter θ of the geometric distribution on the basis of a single obser-vation. If the loss function is given by L[d(x), θ] = c{d(x) − θ}2 and is looked upon as a random variable having the uniform density h(θ ) = 1 for 0 <θ< 1 and h(θ ) = 0 else-where, duplicate the steps in Example 9 to show that (a) the conditional density of given X = x isφ(θ|x) = x(x + 1)θ (1 − θ )x−1 for 0 <θ< 10 elsewhere(b) the Bayes risk is minimized by the decision function d(x) = 2x + 2

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3.6 From the marginal pdf of X, fx (x), in #3.1, give the cumulative distribution function of X, Fx (x). 3.7 Find the following: (a) P[X > 1.2] from the cdf of X in #3.6 (b) P[Y< ½ |X = 1] (refer to #3.3) (c) E[ Y |X = 1 ] (refer to #3.3)