3) Suppose the jornt density of x and x is defined by texigg = { loxge It ocx eyel what is & cxely = y)?
the answer should be 1/2y^2
3. Suppose the joint density of X and Y is defined by if 0<r<y< 1 f(x,y)= elsewhere. What is E (X2Y = ) ?
2. (46 pts) Suppose the random variables X and Y have the joint density function defined by: f(x, y)- otherwise a) Find the value for the constant c b) Find the marginal cdf for X and Y c) Find PiX>3, Y>2)
3. Suppose X and Y have joint density f(x,y)- "cy. 0 < x < y < oo, and equal to 0 for all other (r, y). (a) Calculate the joint density of U = Y-X,V-X. (b) Are U and V independent?
The joint probability density function of X and Yis defined by f(, )0 elsewhere What is Pr(X Y K z,0 1)?
The joint probability density function of X and Yis defined by f(, )0 elsewhere What is Pr(X Y K z,0 1)?
Suppose X~
and Y~
What is the density for X+Y?
Exp(λ) We were unable to transcribe this image
Given a density function defined as: 1) Find the density function of the following variables, what are the types of distribution? X, Y, X|Y=y, Y|X=x 2)find E(Y|X=x) and E(X|Y=y) 3)Calculate E(X) from (2) el se
(1 point) Let X and Y have the joint density function (a) What is the joint density function of U,V? (b) On what domain is this defined? and
(1 point) Let X and Y have the joint density function (a) What is the joint density function of U,V? (b) On what domain is this defined? and
4. (10 marks) Let a lamina of density px, y) = (x + 1)y be defined in the region bounded by the parabolas y = x2 and y = 2 - x?. Find the mass of the lamina.
Show the random variables X and Y are independent, or not
independent
Find the joint cdf given the joint pdf below
Suppose that (X, Y) is uniformly distributed over the region defined by 0 sys1-x2 and -1sx 4 Therefore, the joint probability density function is, 0; Otherwise
Suppose that (X, Y) is uniformly distributed over the region defined by 0 sys1-x2 and -1sx 4
Therefore, the joint probability density function is, 0; Otherwise
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.