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Problem 4 Suppose X ~N(0, 1) (1) Explain the density of X in terms of diffusion process. (2) Calculate E(X), E(X2), and Var(X). (3) Let Y = μ +ơX. Calculate E(Y) and Var(Y). Find the density of Y.
Problem 4 Suppose X ~N(0, 1) (1) Explain the density of X in terms of diffusion process. (2) Calculate E(X), E(X2), and Var(X). (3) Let Y = μ +ơX. Calculate E(Y) and Var(Y). Find the density of Y.
Suppose X ∼ N(0, 1). (1) Explain the density of X in terms of the diffusion process. (2) Calculate E(X), E(X^2 ), and Var(X). (3) Let Y = µ + σX. Calculate E(Y ) and Var(Y ). Find the density of Y.
20. For X let E(X)-0 and sd(x)-2, and for Y let E(Y)--1 and sd(Y)-4. Find: (a) E(X-Y) and E (X Y). (b) Var(X- Y) and Var(X+ Y) if X and Y are independent. (c) EGX+ 흘 Y) and Var(1X+] Y) İf X and Y are independent. (d) Repeat (b) if, instead of independence, Cov(X, Y)- 1. soY is VarY larger
mandan variabds Find (a) E(sx-y〉, (b) Var (SX-y), (c) Cov (3xtYN),a(x,5x-y
Obtain E(Z|X), Var(Z|X) and verify that E(E(Z|X)) =E(Z),
Var(E(Z|X))+E(Var(Z|X)) =Var(Z)
3. Let X, Y be independent Exponential (1) random variables. Define 1, if X Y<2 Obtain E (Z|X), Var(ZX) and verify that E(E(Zx)) E(Z), Var(E(Z|X))+E(Var(Z|X)) - Var(Z)
Let X and Y be random variables with the follow E(Y) μ,--2 Var(x) o, 0.3 Var(Y)-σ,-0.5 Cov(XY) o,,-0.03 Find the following: ESX-3 Y)
Math 180 Exam 3 (Question 9)
9) (7 points) Let f(x)=x°-5x +4. Find all values of c in the interval [ – 2, 3] that satisfy the conclusion of the Mean Value Theorem.
For random variables X, Y, and Z, Var(X) = 4, Var(Y) = 9, Var(Z) = 16, E[XY] = 6, E[XZ] = −8, E[Y Z] = 10, E[X] = 1, E[Y ] = 2 and E[Z] = 3. Calculate the followings: (b) Cov(−3Y , −4Z ). (d) Var(Y − 3Z). (e) Var(10X + 5Y − 5Z).
Let f(x)=5x^2+9 and g(x)=x-4 A) Find the composite function (fog)(x) and simplify. B) Find (fog) (3)
For the random variables X and Y having E(X) = 1, E(Y) = 2, Var (X) = 6, Var (Y) = 9, and Pxy = -2/3. Find a) The covariance of X and Y. b) The correlation of X and Y. c) E(X2) and E(Y2).