Question: Suppose the distribution of Y, conditional on X = x, is n(x, x2) and that the marginal distribution of X is uniform(0,1). (a) Find EY,

Suppose the distribution of Y, conditional on X = x, is n(x, x2) and that the marginal distribution of X is uniform(0,1).
(a) Find EY, Var Y, and Cov(X, Y).
(b) Prove that Y/X and X are independent.

Step by Step Solution

★★★★★

3.34 Rating (184 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a EY EEY X EX 12 VarY Var EY X EVarY X VarX EX 2 112 13 512 E... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

941-M-S-P (8649).docx

120 KBs Word File

Students Have Also Explored These Related Statistics Questions!

Find the marginal distributions and the distribution of Y conditional on X = 0. For the above joint distributions describing the values of the random variables X and Y, find both marginal...

The random variable X has probability distribution Pr(X = 0) = 0.8 and Pr(X = 1) = 0.2. The random variable Y has probability distribution Pr(Y = 1) = 0.3, Pr(Y = 2) = 0.5, and Pr(Y = 3) = 0.2. Find...

The random variable X has probability distribution Pr(X = 0) = 0.3, Pr(X = l) = 0.4, and Pr(X = 2) = 0.3. The random variable Y has probability distribution Pr(Y = 1) = 0.6, Pr(Y = 2) = 0.1, and Pr(Y...

1. Suppose the distribution of Y, conditional on X = x, is N(x, x2) and that the marginal distribution of X is Uniform [0, 1]. (a) Find E[Y], var(Y) and cov(X, Y). (b) Prove that Y/X and X are...

Please provide a step-by-step solutions so I can use it to teach myself. #3-HW 6 (10-13) - STATS #3 3. Suppose that the distribution of Y, conditional on X"= x, is N(x, x2) and that the marginal...

Suppose X and Y are discrete random variables with the following bivariate distribution. f(x,y) Y = 2 Y=9 X=2 0.2 0.1 X=3 0.1 0.1 X-7 0.1 0.4 Find the marginal distribution of Y y f(y) What is the...

Let X have a uniform distribution on the interval (0,1). Given that X = x, let Y have a uniform distribution on the interval (0, x + 1). (a) Find the joint pdf of X and Y. Sketch the region where...

Answer all . 4. The Uris & Warren Ratings Agency rates bonds on a simplified scale with just three categories: A, B, and C. The Professors Pension Fund has all its money invested in two bonds, X and...

Statistics for Strategy Exam 2 Fall 2014 11:30 am Friday Oct. 3 100 points 1. Bubble Sheet: (Fill in 2 items only) (a) Write and bubble your Name (Last name, b First name) (b) Write and bubble your...

Two methods of measuring surface smoothness are used to evaluate a paper product. The measurements are recorded as deviations from the nominal surface smoothness in coded units. The joint probability...

1. Select a country with a stable population and one with a rapidly growing population. Contrast the marketing implications of these two situations. 2. Pick a country and show how employment and...

Use the DuPont system and the following data to find return on equity. Leverage ratio (assets/equity) ......... 2.2 Total asset turnover ............. 2.0 Net profit margin ............. 5.5%...

Find the derivative of f ( x ) = x 1 ( x + 1 ) 2 . 1 . f ( x ) = x 2 + 2 x 3 ( 1 + x ) 2 2 . f ( x ) = 3 + 2 x x 2 ( 1 x ) 2 3 . f ( x ) = x 2 2 x 3 ( 1 x ) 2 4 . f ( x ) = x 3 ( 1 + x ) 3 5 . f ( x...

Do you think the rise in digital ads, which have increased as a result of the COVID-19 pandemic, will change how brands can message their products in different regions? Why or why not?

A random sample of new home sales (in dollars) for a four-bedroom house with 2.5 bathrooms and a two-car garage based on the age of the home and the region of the United States is given in Table...

An investor wants to invest in a mutual fund. She is hoping that the long-term trend for the fund will be increasing. She has data on the mutual fund price collected each month for the years 2016 and...

The data presented in Table 12.10 gives the lifetime (in hours) of cell phone batteries based on the age of the battery and the capacity of the battery (in milliamps per hour). a. Which is the row...

Suppose that X Binomial(n, p): i.e., that X is the sum of the number of successes observed in n independent trials, each of which has success probability p. One can show that the characteristic...

A four - year option - free bond has a par value of R 1 0 0 0 , has an annual coupon rate of 9 percent and trades at a yield to maturity of 7 percent. The current bond price is R 1 0 6 7 . 7 4 . The...

Perform an Even Swap Analysis for the online commerce sites below. Use the following criteria to make swaps 1) As we raise the defect percent by 1%, we reduce costs by $20 2) If we raise service from...