Given the discrete mf of rvx, MrC)22t + 3e3t + 4e"*+5e): a. E(X)? b. Var(X)-?
If the discrete random variable X has a moment generating function given by My(t) = (e'-1) Find E(X + 2x2) and Var(2X + 40).
QUESTION 9 Given E(X)=2 and Var(X)=4, let Y =5X-3. Find E(Y) Var(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)
1. The probability distribution of a discrete random variable X is given by: P(X =-1) = 5, P(X = 0) = and P(X = 1) = ? (a) Compute E[X]. (b) Determine the probability distribution Y = X2 and use it to compute E[Y]. (c) Determine E[x2] using the change-of-variable formula. (You should match your an- swer in part (b). (d) Determine Var(X).
Homework 1 1.1 Given: A=ę, -9e, -e,, B = 2e, -4e, +3e, , please solve the following questions: (1) A:B (2) AXB. Emis, A=e, -9e, - e,, B = 2e-4e, +3e, (1) 8 (2) AB, 1.2 Determine the equation of the isosurface of ø, which passes through the point M (4,1,6), and o is 0 = ln(x² + y2 +z). $ 5° = ln(x² + y2 + 2) t&M (4.1.6) 1989' .
The position of a particle moving along the x axis is given by x = (21 + 22t - 6.0t2) m, where t is in s. What is the average velocity during the time interval t = 1.0 s to t = 3.0 s?-6.0 m/s-4.0 m/s -2.0 m/s-8.0 m/s8.0 m/s
3. Let X be a discrete random variable with the following PMF: 0.1 for x 0.2 for 0.2 for x=3 Pg(x)=〈 0.1 for x=4 0.25 for x=5 0.15 for x=6 otherwise a) (10 points) Find E[X] b) (10 points) Find Var(X) c) Let Y-* I. (15 points) Find E[Y] II. (15 points) Find Var(Y) X-HX 4. Consider a discrete random variable X with E [X]-4x and Var(X) = σ. Let Y a. (10 points) Find E[Y] b. (20 points) Find...
Let X be a discrete random variable whose distribution is given by the table below. W, P(X=w 2 0.01 4 0.40 9 0.32 11 0.27 (the probability that X equals a number outside of the left column is zero) Calculate: 1. E(X) 2 Var(x) 3. PX <4)
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.
der two independent random variables X and Y with the following 11. Consi means and standard deviations: = 60; ơv_ 15. (a) Find E(x + Y), Var(X + Y), E(X Y), Var(X - Y). (b) If x* and Y* are the standardized r.v.'s eorresponding to the r.v.'s X and Y, respectively, determine E(X* + Y*), E(X*-Y*), Var(X* Y*), Var(x* - Y*)
der two independent random variables X and Y with the following 11. Consi means and standard deviations: = 60;...