.Suppose X~Exp(1). Let Y1=e^x andY2=X^2. Calculate the probability density funciton of Y1 and Y2

Question

Question

math Statistics-And-Probability

Answer 1

Answer #1

hii dear i will give my 100% can you please like it.

Answer 2

Similar Homework Help Questions

Let Y1 and Y2 have the joint probability density function given by f(y1, y2) = (...

Let Y1 and Y2 have the joint probability density function given by f(y1, y2) = ( 1, 0 ≤ y1 ≤ 1, 0 ≤ y2 ≤ 1 0, elsewhere.) (a) Show that Y1 and Y2 are independent. (b) What is the covariance Cov(Y1, Y2)?
Let Y1, Y2 have the joint density f(y1,y2) = 4y1y2 for 0 ≤ y1,y2 ≤ 1...

Let Y1, Y2 have the joint density f(y1,y2) = 4y1y2 for 0 ≤ y1,y2 ≤ 1 = 0 otherwise (a) (8 pts) Calculate Cov(Y1, Y2). (b) (3 pts) Are Y1 and Y2 are independent? Prove your answer rigorously. (c) (6 pts) Find the conditional mean E(Y2|Y1 = 1). 3
Let Y1 have the joint probability density function given by and Y2 k(1 y2), 0 s...

Let Y1 have the joint probability density function given by and Y2 k(1 y2), 0 s y1 y2 1, lo, = elsewhere. (a) Find the value of k that makes this a probability density function k = (b) Find P 1 (Round your answer to four decimal places.)

Let Yı, Y, have the joint density S 2, 0 < y2 <yi <1 f(y1, y2)...

Let Yı, Y, have the joint density S 2, 0 < y2 <yi <1 f(y1, y2) = 0, elsewhere. Use the method of transformation to derive the joint density function for U1 = Y/Y2,U2 = Y2, and then derive the marginal density of U1.
2. Let the random variables Y1 and Y, have joint density Ayſy22 - y2) 0<yi <1,...

2. Let the random variables Y1 and Y, have joint density Ayſy22 - y2) 0<yi <1, 0 < y2 < 2 f(y1, y2) = { otherwise Stom.vn) = { isiml2 –») 05451,05 ms one a independent, amits your respon a) Are Y1 and Y2 independent? Justify your response. b) Find P(Y1Y2 < 0.5). on the
Let f(x,y) = exp(-x) be a probability density function over the plane. Find the probabilities: Parta)P(...

Let f(x,y) = exp(-x) be a probability density function over the plane. Find the probabilities: Parta)P( X2 + y2 <a), a > 0, Part b)P(x2 + y2 <a), a > 0.

Let X1, X2, ..., Xn be independent Exp(2) distributed random vari- ables, and set Y1 =...

Let X1, X2, ..., Xn be independent Exp(2) distributed random vari- ables, and set Y1 = X(1), and Yk = X(k) – X(k-1), 2<k<n. Find the joint pdf of Yı,Y2, ...,Yn. Hint: Note that (Y1,Y2, ...,Yn) = g(X(1), X(2), ..., X(n)), where g is invertible and differentiable. Use the change of variable formula to derive the joint pdf of Y1, Y2, ...,Yn.
1. Let (N(t))>o be a Poisson process with rate X, and let Y1,Y2, ... bei.i.d. random...

1. Let (N(t))>o be a Poisson process with rate X, and let Y1,Y2, ... bei.i.d. random variables. Fur- ther suppose that (N(t))=>0 and (Y)>1 are independent. Define the compound Poisson process N(t) Y. X(t) = Recall that the moment generating function of a random variable X is defined by ºx(u) = E[c"X]. Suppose that oy, (u) < for all u CR (for simplicity). (a) Show that for all u ER, ºx() (u) = exp (Atløy, (u) - 1)). (b) Instead...
Let Y1 and Y2 be two independent discrete random variables such that: p1(y1) = 1/3; y1...

Let Y1 and Y2 be two independent discrete random variables such that: p1(y1) = 1/3; y1 = -2 ,- 1, 0 p2(y2) = 1/2; y2 = 1, 6 Let K = Y1 + Y2 a) FInd the moment Generating function of Y1, Y2, and K b) find the probability mass function of K

1. Suppose X1, ..., Xn be a random sample from Exp(1) and Y1 < ... <...

1. Suppose X1, ..., Xn be a random sample from Exp(1) and Y1 < ... < Yn be the order statistics from this sample. a) Find the joint pdf of (Y1, .. , Yn). b) Find the joint pdf of (W1, .. , Wn) where W1 = nY1, W2 = (n-1)(Y2 -Y1), W3 = (n - 2)(Y3 - Y2),..., Wn-1 = 2(Yn-1 - Yn-2), Wn = Yn - Yn-1. (c) Show that Wi's are independent and its distribution is identically...