(f) Consider the pair of discrete random variables X, Y with joint PMF described below: 3 У Px,y(x, y) 0 -2 -1 +1 +2 1/12 1/6 0 x 1 1/3 0 1/6 2 1/12 1/12 1/12 Compute E[XY²] and E[Y³|X = 0].
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![(f) Consider the pair of discrete random variables X, Y with joint PMF described below:
3
У
Px,y(x, y)
0
-2
-1
+1
+2
1/12
1/6
0
x
1
1/3
0
1/6
2
1/12 1/12 1/12
Compute E[XY²] and E[Y³|X = 0].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F02681530-b6ca-4d72-bfd1-7260256101ab%2F491b83b5-e5bc-4f9f-9aa5-35c1148be58b%2F57opqnh_processed.png&w=3840&q=75)
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- X and Y are discrete random variables. If var(X)= var(Y) = o², cov(X,Y)=, find var(2X-3Y)Let X, Y and Z be three independent random variables such that E(X)=E(Y)=E(Z)=1 and E(X2)-E(Y²)=2E(Z²)=10. Then Var(X+Y+Z) is equal to:Let X be a random variable such that E(X²) a. V(3X-3) b. E(3x-3) = 58 and V(X) = 40. Compute
- Suppose X and Y are independent random variables with E(X) =2, E(Y)=3,V(X)=4,V(Y)=16. Finda)E(5X-Y) b)V(5X-Y) c)COV(3X+Y,Y) d)COV(X,5X-Y)Let us say that we have jointly distributed random variables X and Y with E(X) = 3,E(Y) = 5, Var (X) = 1, Var(Y) = 3, and Cov (X, Y) = 2.Determine:a) E(2X + Y) b) Var(6X)Suppose that X and Y are random variables with E(X) = 2, E(Y) = 5 and E(X) = 8, E(Y) = 30 and cov(X + 2Y,-3X+ 4Y) = -12, then cov(2X +3,-3Y +4) is equal to: Hint: cov(aX + bY.cX + dY) = acV(X) + bdV(Y) + (bc + ad)cov(X, Y) -59 O -120 -64 -30
- Q3/(a) Let X = b(n, ) and E(x)=E(16–7x) find n. (b)Let X be a random variable with p.d.f, f(x)=c x =1,2,3,.., zero elsewhere. Find the constant c.X is a continuous random variable having p.d.f. f(x) such that f(x) = kr Osx55 otherwise Find : (a) the constant k; (b) P(15XS 2); (c) (d (e) (f) E(X); E(3X + 1); E(X?); Var (X); (g) Var (4X - 5);Let X be a random variable and a real number. Show that E(X - a)² = varX + (µ − a)² Hereμ = EX is the expected value of the random variable X and varX = E(X - μ)^2 is the variance of the random variable X. Guidance: start from the representation - (X-a)^2 = (X µ + μ- a)^2 and group the right side of the representation appropriately into the form (Z + b)^2, where Z is some random variable and b is a real number and open the square. The task should be solved with the help of the expected value calculation rules.
- Suppose that X and Y are random variables with E(X) = 2 , E(Y) = 5 and E(X²) = 8, E(Y?) = 30 and cov(X – 2Y,3X – 4Y) = -12, then cov(2X – 3, –5Y + 4) is equal to: Hint: cov(aX + bY,cx + dY) = acV(X) + bdV(Y) + (bc + ad)cov(X,Y) -59 -120 -64 -30Q3/(a) Let X = b(n,) and E(x)= E(16-7x) find n. (b)Let X be a random variable with p.d.f, ƒ(x)= c 3 x=1,2,3,.., zero elsewhere. Find the constant c.Consider two independent exponential random variables X1 and X2 with parameter lambda=1. LetY1 = X1 Y2 = X1 + X2. Find the MMSE estimate of Y1 using Y2.
