Question 1 (1 point) If two random variables (X & Y) are independent, then according to...
4. Consider two independent random variables X and Y, such that E[X] = 1 E[Y] = 2 var(X) = 2 var(Y) = 1 Let Z = X-Y 2 (a) Calculate E[2] (b) Calculate var(Z). 3
Let X and Y be two independent random variables such that E(X) = E(Y) = u but og and Oy are unequal. We define another random variable Z as the weighted average of the random variables X and Y, as Z = 0X + (1 - 0)Y where 0 is a scalar and 0 = 0 < 1. 1. Find the expected value of Z , E(Z), as a function of u . 2. Find in terms of Oy and...
Let X and Y be two independent random variables. Show that Cov (X, XY) = E(Y) Var(X).
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).
X and Y are random variables (a) Show that E(X)=E(B(X|Y)). (b) If P((X x, Y ) P((X x})P({Y y)) then show that E(XY) = E(X)E(Y), i.e. if two random variables are independent, then show that they are uncorrelated. Is the reverse true? Prove or disprove (c) The moment generating function of a random variable Z is defined as ΨΖφ : Eez) Now if X and Y are independent random variables then show that Also, if ΨΧ(t)-(λ- (d) Show the conditional...
Question 7 (1 point) Suppose we have the following values for variables X (independent) and Y (dependent) IX-X)(y-7) --630 Z(X - x)2 = 168 SSE = 1225 SSR = 2362.5 What is the value of R-Square (round to four decimal places)? Question 8 (1 point) Suppose we have the following values for variables X (independent) and Y (dependent) EIX-XIY-7)=-630 IIX Xj2 = 168 SSE = 1225 SSR = 2362.5 What is the value of the slope coefficient for the simple...
Let X and Y be independent identically distributed random variables with means µx and µy respectively. Prove the following. a. E [aX + bY] = aµx + bµy for any constants a and b. b. Var[X2] = E[X2] − E[X]2 c. Var [aX] = a2Var [X] for any constant a. d. Assume for this part only that X and Y are not independent. Then Var [X + Y] = Var[X] + Var[Y] + 2(E [XY] − E [X] E[Y]). e....
solution please 2. If X and Y are two random variables with Var(X) = 36, Var(Y) = 16, and Cov(X,Y) = 24, what is ρXY, the correlation coefficient between X and Y? (A) -1 (B) 0 (C) 1/24 (D) 1
Question 3 [17 marks] The random variables X and Y are continuous, with joint pdf 0 y otherwise ce fxx (,y) a) Show that cye fr (y) otherwise and hence that c = 1. What is this pdf called? (b) Compute E (Y) and var Y; (c) Show that { > 0 fx (a) e otherwise (d) Are X and Y independent? Give reasons; (e) Show that 1 E(XIY 2 and hence show that E (XY) =. Question 3 [17...
Problem D: Suppose X1, .,X, are independent random variables. Let Y be their sum, that is Y 1Xi Find/prove the mgf of Y and find E(Y), Var(Y), and P (8 Y 9) if a) X1,.,X4 are Poisson random variables with means 5, 1,4, and 2, respectively. b) [separately from part a)] X,., X4 are Geometric random variables with p 3/4. i=1