Indication: Ex 9.19 of tertbook. Let X and Y be two continuous random variables withjoint density function8.30 -50z -50y +80zyf(r, y) =-e1. Determine the marginal distributions of X and Y.2. Find out Var(X), Var(Y) and correlation coefficient p p(X,Y)3. Find the real value a so that Cou(X+aY, Y)=0.4. Determine the density function of X +Y.5. (Bonus) Find the joint probability density function of (X+aY, Y) with a obtainedin the question 2. And deduce that X+aY and Y are independent.

Rewrite the above equation and just compare this f(x,y)=k*e{-12(ax2-2hxy+by2)} ,…

Answered: 8 Indication: Ex 9.19 of tertbook. Let…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.3: Least Squares Approximation

Problem 32EQ

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A Troublesome Snowball One winter afternoon, unbeknownst to his mom, a child bring a snowball into the house, lays it on the floor, and then goes to watch T.V. Let W=W(t) be the volume of dirty water that has soaked into the carpet t minutes after the snowball was deposited on the floor. Explain in practical terms what the limiting value of W represents, and tell what has happened physically when this limiting value is reached.
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.)
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 ?
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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)Find the conditional pdf of x given that y = Y,px|y(X|Y):b)Calculate E[x|y = Y], to 0<=Y<=1.c)Calculate Var [ x|y = Y], to 0 <= Y <= 1.
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).

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