Suppose A B C be random variable with
E[A] = 3 and E [A^2]= 10
Var[B] = 5, E[C] = 2
E [c^2] = 7 we know A and B are independent
E[AC] = 5
Cov(B, C) = 2 please find Var[3A +B - C]
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Suppose A B C be random variable with E[A] = 3 and E [A^2]= 10 Var[B]...
(1 point) For a random variable X, suppose that E[X] = 2 and Var(X) = 3. Then (a) E[(5 + x)2) = (b) Var(2 + 6X) =
Let X, Y, Z be random variables with these properties: · E[X] = 3 and E[X²] = 10 Var(Y) = 5 E[Z] = 2 and E[Z2] = 7 • X and Y are independent E[X2] = 5 Cov(Y,Z) = 2 Find Var(3X+Y – Z).
3. Let X be a continuous random variable with E(X)-μ and Var(X)-σ2 < oo. Suppose we try to estimate μ using these two estimators from a random sample X, , X,: For what a and b are both estimators unbiased and the relative efficiency of μι to is 45n?
Please answer both.
. Suppose that Y is a random variable with distribution function below. 1-e-v/2, 0, y > 0; otherwise F(y) = (a) Find the probability density function (pdf) f(y) of Y. yso (b) E(Y) and Var(Y) 5. Suppose X is a random variable with E(X) 5 and Var(X)-2. What is E(X)?
2. Suppose the variables Yi and Y have the following properties EQİ)-4, Var(h)-19, E(Y )-6.5, Var(Ya)-5.25, E(Y3%)-30 Calculate the following; please show the underlying work a) (3 pts) Cov(, ) b) (3 pts) Cov(41, 3%) c) (3 pts) Cov(41.5-½) (6 pts) Find the correlation coefficient between 1 + 3, and 3-2%
X,Y, and Z are random variables.
Var(X) = 2, Var(Y) = 1, Var(Z) = 5, Cov(X,Y) = 3, Cov(X, Z) = -2, Cov(Y,Z) = 7. Determine Var(3X – 2Y - 2+10)
6 Suppose that X and Y are random variables such that Var(X) Var(Y)-2 and Cov(x,y)- 1. Find the value of Var(3.X-Y+2)
please show steps, thank you (Sec. 5.2, 00) Suppose X and Y are independent random variables with E[X] = 6, E[Y ] = −3, Var[X] = 9, and Var[Y ] = 25. Find: (a) E[2Y − X] (b) Var[2Y − X] (c) Cov[X, Y ] (d) ρ[X, Y ] (e) Cov[5X + Y, Y ] (f) Cov[X, 2Y − X]
6 Suppose that X and Y are random variables such that Var(X)-Var(Y)-2 and Cov(x,y)- 1. Find the value of Var(3.X-Y + 2)
Problem 2 Suppose two continuous random variables (X, Y) ~ f(x,y). (1) Prove E(X +Y) = E(X)+ E(Y). (2) Prove Var(X + Y) = Var(X) + Var(Y)2Cov(X, Y). (3) Prove Cov(X, Y) E(XY)- E(X)E(Y). (4) Prove that if X and Y are independent, i.e., f(x, y) Cov(X, Y) 0. Is the reverse true? (5) Prove Cov (aX b,cY + d) = acCov(X, Y). (6) Prove Cov(X, X) = Var(X) fx (x)fy(y) for any (x,y), then =