16. Two random variables X and Y take the values 1,2,3 along the probabilities shown below:KK2KK2K3.2KK2K(i)(ii)(ii)Find K.Find E(X+Y)Find Var (X), Cov (X,Y)(iv)Find the conditional distribution of Y given that X = 3.

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Answered: 16. Two random variables X and Y take…

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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2. Let X ~ N(0, o²) and Y ~ (0, v²) be independent random variables and Z = X + Y. (a) Find the LMMSE estimator of X given Z. (b) Find the conditional distribution fz|x(z, x). (c) Using the previous part, find the conditional distribution fx|z(x, z). (d) Find the MMSE estimator of X given Z and show that it is the same as the LMMSE estimator in Part (a).
Let X and Y be any two random variables and let a and b be any two real numbers. Then var(ax + bY) = a² var(X) + b?var(Y) + 2ab cov(X,Y). False True
Suppose that X, Y, and Z are jointly distributed random variables, that is, they are defined on the same sample space. Suppose that we also have the following. E(X)=0 Var(X) = 39 Var(Y) = 19 Var(Z) =24 E(Y) =-4 E(Z)=6 Compute the values of the expressions below. E(1+5z) = -Y-4Z E 2 Var(4–3Y) = I E(sz²) = I
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17
Let random variable X be the number of users communicating with a cellular base station within a given time interval. Its PMF is :
Let X1, X2, . . . are independent indicator variables with different probabilities of success. That is, P(Xi = 1) = pi. Define Yn = X1 + X2 + . . . + Xn. Find E(Yn), V ar(Yn) and coefficient of variation of Yn
A random point (X,Y) is distributed uniformly on the square with vertices (1,1), on the square. (1,-1), (-1, 1), and (-1,-1). That is, the joint pdf is f(x,y) Determine the probabilities of the following events. (a) x² + y² 0 (c) |X+Y| < 2
2. Let the independent random variables X1 and X2 have Bin(0.1,2) and Bin(0.5, 3), respectively. (a) Find P(X1 = 2 and X2 = 2). (b) Find P(X1 + X2 = 1). (c) Find E(X1 + X2). (d) Find Var(X1 + X2).
Let X and Y denote two random variables. Which of the following can be used to compute Var(X)? A. E[Var(X|Y)] + Var(Var(X|Y)) B. E[E[X|Y]] + Var(Var(X|Y)) C. E[Var(X|Y)] + Var(E[X|Y]) D. Var(E[X|Y]) + Var(Var(X|Y))

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16. Two random variables X and Y take the values 1,2,3 along the probabilities shown below: 3 Y K K 2K K 2K K 3. 2K K 2K (i) Find K. (ii) (ii) (iv) Find E(X+Y) Find Var (X), Cov (X,Y) Find the conditional distribution of Y given that X 3.