If Xis a continuous random variables, then Cov(x,x)(a) o(b)o(c)Hv(d)None of them15- If X and Y are two continuous random variables, then ix-x--(a) [xx-4)(c) joix-xx(d) IxGx-XldyIf X and Y are two discrete random variables, then y(a) [Σ*(*)(b) [(y)(d) I7417- If X is a continuous random variable, then Cov(x, 2 x)=(a) 4E(xả)(b) 2E(x²)-2(E(x))²@4[E(x²)-(E(x))*](c) ox18- If E(x) = 1 and E (x²)=5, then p(x,x)=......(a) 1(b) 2(d) 0(c)-119. If X and Y have trinomial distribution with parameters (.p.p.), then the marginalprobability mass function of X'is given by f(x).......(a)x²(a-x)"P:(1-P)**(b)0-Ax(n-x)"n!d(c)(d)PO-P₂)x-x)!x!(-x)20- If X and Y are independent random variables, then Co(x,y).....(a) o(b) σ(c)(d)116-#₂

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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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17. Let die die = {(W₁ W₂) : w₁ = 1, 2, 3, 4, 5, 6; w₂= 1,2,3,4,5,6} and consider two random variables X(W₁=W₂) =W₁ + W₂= Y(w₁, W₂) = W₁ - W₂. Compute Cov(X, Y). Are they independent?
Let X be a random variable defined by 2 3 P(X = x) k 2k 2k 2k 2k Then E(X) and V(X) are equal to: None of these O E(X)=13/5 and V(X)=41/25 O E(X)=20/9 and V(X)=140/81 O E(X)=27/11 and V(X)=206/121
4. Suppose we have random variables W and Q, and we know Var(W) = 25, Var(Q) = 10, and Cov(W, Q) = 2. Now, let A = 2W + 4Q. What is Var(A)?
For a discrete random variable X, find Var(X) if* Var (5 - 2X) = 12 a)2 b)1 c)3 d)6
(a) Let X, Y be independent random variables with respective PMFS Px(x) = (-) )* > Py (Y) = (-) )", y=1, 2, 3, . . . .2 , х-0, 1, 2, 3, . . Find P(X+Y=3)
20
Let (X1, X2, X3) be the random outcome of tossing a fair six-faced die three times, and let (Y(1), Y(2), Y(3) be the order statistics from (X1, X2, X3). We have Y(1) = min (X1, X2, X3), Y(3) = max (X1, X2, X3), and Y(1) < Y(2) < Y(3). Find Pr (Y(1) = 3).
If A and B are events for which P(A U B) = 1,then P(A' U B') = a) 1 b) Р(А') + P(В") c) P(A) + P(Β') - 1 d) 0 e) P(A') + P(B') – P(A') · P(B')
The joint probability function of two discrete random variables X and Y is given by Ax,y) = c(2x+y), where x and y can assume all integers such that 0< x
-) Suppose X and Y are continuous random variables. The range of X is [1,3], the range of Y is [0, 1]. The joint pdf of X and Y be given by f(x, y) = 2xy³ - 2y³. Verify if X and Y independent random variables.
24. Gaussian random variables X, and X,, for which, X, = 2, o = 9, X, =-1, ox, = 4 and Cxx, =-3, are transformed to new random variables Y, and Y, according to जापर डेरें| Y, =-X, + X, Y, =-2X,- 3X, (iii) Cy,Cy, .. Find
Suppose we choose arbitrarily a point from the square with corners at(2,1), (3,1), (2,2), and (3,2). The random variable A is the area of the trianglewith its corners at (2,1), (3,1), and the chosen point. Compute E[A].

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If X is a continuous random variables, then Covs.) (a) o (b) , (c) P (d)) None of them as- If X and Y are two continuous random variables, then ix--- (a) voix-x) (b)) Exox-x) (e) jroix- (d) Joix-dy 16- If X and Y are two discrete random variables, then y (b) Exten (a) f(x)