Suppose X Exponential(1) and given X = x, Y is a uniform random variable in [0,x]

Question:

Suppose X ∼ Exponential(1) and given X = x, Y is a uniform random variable in [0,x] , i.e., Y |X = x ∼ Uniform(0, x), or equivalently Y |X ∼ Uniform(0,X).

a. Find EY.

b. Find Var(Y).

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For answer-question

Introduction To Probability Statistics And Random Processes

ISBN: 9780990637202

1st Edition

Authors: Hossein Pishro-Nik

See More Books

Question Posted: Oct 27, 2023 03:32 AM

See More Questions

Suppose a random variable has some PDF given by fX(x). Find a function g(x) such that Y= g(X) is a uniform random variable over the interval (0, 1). Next, suppose that X is a uniform random variable....
Suppose U is a uniform random variable over [0, 1]. (a) Show that Y =(ba)U +a is uniform over [a, b]. (b) Use part (a) and Question 3.6.4 to find the variance of Y .
A uniform random variable has a PDF given by fX (x) = u(x) u (x 1). (a) Find the mean and variance of X. (b) Find the conditional mean and the conditional variance given that 1 / 2 < X < 3 / 4.
Local 54 has retained James Love to represent it in a grievance against Dilated Peoples Optical Inc. The union is grieving the employers decision to exclude from the bargaining unit the position of...
How can firms use marketing public relations (MPR) to their advantage?
Find two different spanning trees for each graph in Problems 1320. A E B D F I J G H
It would be helpful to me if I could start by asking you to basically tell me about your job. Okay?
Olive Corporation was formed and began operations on January 1, 2018. The corporations income statement for the year and the balance sheet at year-end are presented below. The corporation made...
8) What does the following method do? Rewrite it so it produces the same results but does not use recursion. public static boolean whoKnows (int arr, int i, int j) { if (i >= j) { return true; } else...
Consider the unit disc D = {(x, y)|x 2 +y 2 1}. Suppose that we choose a point (X, Y) uniformly at random in D. That is, the joint PDF of X and Y is given by a. Find the constant c. b. Find the...
Let X and Y be two independent Uniform(0, 1) random variables. Find P(X 3 + Y > 1).
Use the graph to find the limit (if it exists). If the limit does not exist, explain why. (a) lim x3 g(x) (b) lim x0 g(x) g(x) = -3 -2x x-3 9 6 3- -6 -9 y 3 6
Initial Public Offerings Research has shown that managers of newly listed firms rein in their capital expenditure plans if the market share price performance is not particularly strong around the IPO...
Explain the following limits on the prices of warrants: (a) If the share price is below the exercise price of the warrant, the lower bound on the price of a warrant is zero. (b) If the share price is...
Carlyle plc and Mullan plc have both announced IPOs at 40 per share. One of these is undervalued by 11, and the other is overvalued by 6, but you have no way of knowing which is which. You plan on...
Why do you think companies have issued bonds in different currencies, maturities and coupon rates? Shouldnt the coupon be the same on every bond? Explain.
Investment Gurus Warren Buffett and several other investors earned significantly positive returns during the financial crisis, 20082009. How can you explain this using the efficient markets...
Watson, Inc., purchased 60 percent of Houston, Inc., on January 1, 2008, for $400,000 in cash. On that date, assets and liabilities of the subsidiary had the following values: On December 31, 2011,...
Linda Lopez opened a beauty studio, Lindas Salon, on January 2, 2011. The salon also sells beauty supplies. In January 2012, Lopez realized she had never filed any tax reports for her business and...
Describe the four types of teams.
Describe the three main components of effective teams.
How can managers help individuals become team players?
In your opinion or what are your thoughts - how important are professional designations/organization in completing fraud and loss investigations?
some instruments in the takht ensemble perform an ostinato underneath a solo instrument. What is an ostinato? Explain.
1. Shika is a single mother and is a 2024 BCom graduate from the National University of Fiji. Soon after graduation, she found a job as an assistant accountant at Naivini Island Resort with the...

Suppose X Exponential(1) and given X = x, Y is a uniform random variable in [0,x]

Question:

Step by Step Answer:

To find the expected value mean and variance of the random variable Y when conditioned o...View the full answer

Introduction To Probability Statistics And Random Processes

Students also viewed these Business questions