E(x) =xP(x) =3*0.6+9*0.4 =5.4
E(x2)=x2P(x) =3^2*0.6+9^2*0.4 =37.8
Var(x)=E(x2)-(E(x))2 =37.8-5.4^2 =8.64
suppose X=3 with probabiltiy 0.6 and X=9 with probability 0.7. obtain E[x] and Var[X] probabilriy .6...
1 0.7 Find the Expected value and the variance of X. E (X)=EXP(X) Var(x)-o? And -E(x?)-me a) Note: = px E(X2)-DFP(%) b) Consider the following information for a binomial N- number of trials or experiments-5 distribution: x-number of success -3 Probability of uccess-sp- 04 and probability of filur 1p-0.6 Find the probability of 3 successes out of 5 trials: Note P(x): Nex px (1-p)NX Note: Nex NI / x! (Naji
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)
р 9. If (X,Y) are bivariate normal with E(X) = 20, var(X) = 25, E(Y) = 16, var(Y) = 9, and = 0.7, what is the distribution of Y given X = 30? 3.52 .d.
The random variable X has the probability density function (x)a +br20 otherwise If E(X) 0.6, find (a) P(X <름) (b) Var(x)
QUESTION 9 Given E(X)=2 and Var(X)=4, let Y =5X-3. Find E(Y) Var(Y)
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).
(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) =
Suppose X has a geometric distribution with probability 0.3 of success and 0.7 of failure on each observation. The probability that X = 4 is(a) 0.0081(b) 0.0189(c) 0.1029(d) 0.2401(e) None of the above.
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.
probability course 01) 6 and Let X and Y be two independent random variables. Suppose that we know Var(2X-Y) Var(X+ 2Y) 9, Find Var(X) and Var(Y).