your mistake is:
For calculation of E(Y) you used directly distribution function. Inplace of that you have to use density of 'y'
I don’t understand where I messed up on these Question 6, (20 pts.) Let f(z)-,-1 <...
6 (20 pts). Let F(x, y, z) = x2 + y2 + x2 - 6xyz. (1) Find the gradient vector of F(x, y, z); (2) Find the tangent plane of the level surface F(x, y, z) = x2 + y2 + x2 - 6xyz = 4 at (0, 0, 2); (3) The level surface F(x, y, z) = 4 defines a function z = f(x,y). Use linear approxi- mation to approximate z = = f(-0.002,0.003).
provided that tihe expettauIO 1.8.10. Let f(z) = 2r, 0 < z < i, zero elsewhere, be the pdf of X. (a) Compute E(1/X). (b) Find the edf and the pdf of Y 1/X c) Compute E(Y) and compare this result with the answer obtained in Part (a).
Problem 3 Let X be Uniform(0,1) and Y be Exponential (1). Assume that X and Y are independent. i. Find the PDF of Z- X +Y using convolution. ii. Find the moment generating function, øz(s), of Z. Assume that s< 0. iii. Check that the moment generating function of Z is the product of the moment gen erating functions of X and Y
Problem 3 Let X be Uniform(0,1) and Y be Exponential (1). Assume that X and Y are...
Let X be a random variable with CDF z<0 G()=/2 0 <IS2 z>2 1 Suppose Y = X2 is another random variable, find (a) P(1/2 X 3/2), (b) P(1s X< 2) (c) P(Y X) (d) P(X 2Y). (f) If Z VX, find the CDF of Z. (d) P(X+Y 3/4)
(b) Let X have the pdf x? f(x)= ;-3<x<3, 18 = zero elsewhere. (i) Find the cdf of X
Can we find this without use of the moment
generating function?
3. (15 pts) Let Xị and X2 be two independent random variables that follow standard normal distribution. The PDF of a standard normal distribution is given by f(t)= exp-/2; - <t<0.. i) Find the joint PDF of V = X1 + X2 and Y2 = X1 - X). ii) Prove that Yi and Y2 are independent. R ONALEN SON
9. Let a random variable X follow the distribution with pdf f(z)=(0 otherwise (a) Find the moment generating function for X (b) Use the moment generating function to find E(X) and Var(X)
What is the moment generating function of the random variable Y = 2X + 1, where X has the pdf f(x) = x/2 , 0 < x< 2, zero elsewhere?
provided that tihe expettauIO 1.8.10. Let f(z) = 2r, 0 < z < i, zero elsewhere, be the pdf of X. (a) Compute E(1/X). (b) Find the edf and the pdf of Y 1/X c) Compute E(Y) and compare this result with the answer obtained in Part (a).
provided that tihe expettauIO 1.8.10. Let f(z) = 2r, 0
(a) If var[X o2 for each Xi (i = 1,... ,n), find the variance of X = ( Xi)/n. (b) Let the continuous random variable Y have the moment generating function My (t) i. Show that the moment generating function of Z = aY b is e*My(at) for non-zero constants a and b ii. Use the result to write down the moment generating function of W 1- 2X if X Gamma(a, B)
(a) If var[X o2 for each Xi (i...