Find E(Y4 ) if the pdf of Y is fY(y)=3e-3y, y≥0.
(10 points) Let Y have probability density function (pdf) 3y?, for ( <y<1 fy(y) = 10, otherwise (a) Compute the probability density function (pdf) of 1/Y. (b) Compute the probability density function (pdf) of Y1 +Y2, if Yį and Y2 are inde- pendent random variables with the same pdf as Y. (You can use a computer to help with the integration).
If fY(y) = 3y^2e^(-y^3) for y>0 what are the principles for finding E[Y] ? (ie what to ask Wolfram Alpha for integration)
Suppose X and Y have the joint pdf f (x, y) = 3y, 0 < y < 1, y − 1 < x < 1 − y 0 otherwise a) Give an expression for P (X > Y ). b) Find the marginal pdfs for Y . c) Find the conditional pdf of X given Y = y, where 0 < y < 1. d) Give an expression for E[XY ]. e) Are X and Y independent?
The joint pdf of X and Y is fxy(x,y) = cx^3y, 0 < x < y < 1 a.) Find the value of c to make this a valid pdf. b.) Are x and y independent?
Please show all work, will rate immediately ??
find and sketch the marginal pdf fY(y)
The Joint distribution function for two rondom variables X and Y is Exy(x, y) = u(x)u(y) [l-e ax cara e acx+y)] where azo Find and sketch the marginal Pdf Fy (4)
f(y)= 3y^2/theta^3 from 0<y<theta, o otherwise. a) Find the pdf of Y(n)= max(Y1,Y2,...,Yn) b) if n=11 find E(Y(n)) c) if n=11 find the pdf of the median
Use undetermined coefficients to find the particular solution to y''+3y'-4y=3e^t
Find the solution of the given IVP y" + 3y' + 2y = uz(t); y(0) = 0, y'(0) = 1 a. y = et-e-t + uz(t) [] + e-(6+2) +22(6+2) b. y = ef +e-t+uz(t)ſ - e-(6-2) + şe-26-2)] + uz(t) - e-(1-2) 3e=2(-2)] e + C. y = e-t-e-27 d. None of these
4. Suppose X and Y have the joint pdf f(x,y) = 6x, 0 < x < y < 1, and zero otherwise. (a) Find fx(x). (b) Find fy(y). (c) Find Corr(X,Y). (d) Find fy x(y|x). (e) Find E(Y|X). (f) Find Var(Y). (g) Find Var(E(Y|X)). (h) Find E (Var(Y|X)]. (i) Find the pdf of Y - X.
Let (X, Y) have joint pdf given by f(r, y)= < a, 0 < < 0, О.w., (a) Find the constant c (b) Find fx(x) and fy(y) (c) For 0 x< 1, find fyx=r (y) and py|x=x and oyx= (d) Find Cov(X, Y) (e) Are X and Y independent? Explain why