Question

In: Statistics and Probability

Let ?1 and ?2 have the joint pdf f (?1, ?2)= 6?2     0<?2<?1<1 =0 else where...

Let ?1 and ?2 have the joint pdf
f (?1, ?2)= 6?2     0<?2<?1<1
=0 else where
A. Find conditional mean and conditional variance ?1given?2
.
B. Theorem of total mean and total variance?1given?2
.(urgently needed)

Solutions

Expert Solution


Related Solutions

Let Y1 and Y2 have joint pdf f(y1, y2) = (6(1−y2), if 0≤y1≤y2≤1 0, otherwise. a)...
Let Y1 and Y2 have joint pdf f(y1, y2) = (6(1−y2), if 0≤y1≤y2≤1 0, otherwise. a) Are Y1 and Y2 independent? Why? b) Find Cov(Y1, Y2). c) Find V(Y1−Y2). d) Find Var(Y1|Y2=y2).
Let (A,B) have joint PDF f(a,b)=(ca^2b^2 when 0 < a,b,a+b < 1 and 0 otherwise for...
Let (A,B) have joint PDF f(a,b)=(ca^2b^2 when 0 < a,b,a+b < 1 and 0 otherwise for some constant c > 0. 1. Find a formula for E[A | B = b]. 2. Find Cov(A,B).
Let X1 and X2 have the joint pdf f(x1,x2) = 2 0<x1<x2<1; 0.  elsewhere (a) Find the...
Let X1 and X2 have the joint pdf f(x1,x2) = 2 0<x1<x2<1; 0.  elsewhere (a) Find the conditional densities (pdf) of X1|X2 = x2 and X2|X1 = x1. (b) Find the conditional expectation and variance of X1|X2 = x2 and X2|X1 = x1. (c) Compare the probabilities P(0 < X1 < 1/2|X2 = 3/4) and P(0 < X1 < 1/2). (d) Suppose that Y = E(X2|X1). Verify that E(Y ) = E(X2), and that var(Y ) ≤ var(X2).
Let X and Y have the joint pdf f(x, y) = 8xy, 0 ≤ x ≤...
Let X and Y have the joint pdf f(x, y) = 8xy, 0 ≤ x ≤ y ≤ 1. (i) Find the conditional means of X given Y, and Y given X. (ii) Find the conditional variance of X given Y. (iii) Find the correlation coefficient between X and Y.
(a) Let X and Y have the joint pdf ???(?, ?)=1, 0≤x≤3/2, 0≤y≤1, zero elsewhere. Find:...
(a) Let X and Y have the joint pdf ???(?, ?)=1, 0≤x≤3/2, 0≤y≤1, zero elsewhere. Find: 1 The pdf of Z=X+Y 2 The pdf of Z=X.Y
Let X and Y be continuous random variables with joint pdf f(x, y) = kxy^2 0...
Let X and Y be continuous random variables with joint pdf f(x, y) = kxy^2 0 < x, 0 < y, x + y < 2 and 0 otherwise 1) Find  P[X ≥ 1|Y ≤ 1.5] 2) Find P[X ≥ 0.5|Y ≤ 1]
Find the probability P(0<X1<1/3 , 0<X2<1/3) where X1, X2 have the joint pdf                    f(x1, x2)...
Find the probability P(0<X1<1/3 , 0<X2<1/3) where X1, X2 have the joint pdf                    f(x1, x2) = 4x1(1-x2) ,     0<x1<1 0<x2<1                                       0,                  otherwise (ii) For the same joint pdf, calculate E(X1X2) and E(X1 + X2) (iii) Calculate Var(X1X2)
Let X and Y have joint pdf f(x,y)=k(x+y), for 0<=x<=1 and 0<=y<=1. a) Find k. b)...
Let X and Y have joint pdf f(x,y)=k(x+y), for 0<=x<=1 and 0<=y<=1. a) Find k. b) Find the joint cumulative density function of (X,Y) c) Find the marginal pdf of X and Y. d) Find Pr[Y<X2] and Pr[X+Y>0.5]
Let X and Y have the joint probabilitydensity function (pdf):?(?, ?) = 3/2 ?2(1...
Let X and Y have the joint probability density function (pdf):   f(x, y) = 3/2 x2(1 − y),        − 1 < x < 1,      − 1 < y < 1 Find P(0 < Y < X). Find the respective marginal pdfs of X and Y. Are X and Y independent? Find the conditional pdf of X give Y = y, and E(X|Y = 0.5).  
Let the joint p.d.f f(x,y) = 1 for 0 <= x <= 2, 0 <= y...
Let the joint p.d.f f(x,y) = 1 for 0 <= x <= 2, 0 <= y <= 1, 2*y <= x. (And 0 otherwise) Let the random variable W = X + Y. Without knowing the p.d.f of W, what interval of w values holds at least 60% of the probability?
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT