Question: Suppose that the range of the continuous variables X and Y is 0 < x < a and 0 < y < b. Also suppose

Suppose that the range of the continuous variables X and Y is 0 < x < a and 0 < y < b. Also suppose that the joint probability density function f_XY(x, y) = g(x)h(y), where g(x) is a function only of x, and h(y) is a function only of y. Show that X and Y are independent.

Step by Step Solution

★★★★★

3.50 Rating (170 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

The marginal density of X is b fx x gxhudu gx h... 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

Students Have Also Explored These Related Applied Statistics and Probability Questions!

Complete the following challenge and upload your screenshot proof. 1. You won't be given many tips on this but you should be able to figure it out. 2. Show evidence of a successful three way...

Suppose that the random variables X and Y have joint PDF That is, X and Y are uniformly distributed over the square 0 ( x ( 2, 0 ( y ( 2. Find (a) The joint PDF of U = X + Y and V = X - Y, and (b)...

Suppose that the random variables X and Y have a joint probability density function f(x, y) = 4x(2 - y) for 0 x 1 and 1 y 2. (a) What is the marginal probability density function of X? (b) Are...

Suppose that the joint p.d.f. of two random variables X and Y is as follows: Determine (a) The value of the constant c; (b) Pr(0 X 1/2); (c) Pr(Y X + 1); (d) Pr(Y = X2). f(x,y-tor' +y) for 0ys1...

Suppose that the range of the continuous variables X and Y is 0 x a and 0 y b. Also suppose that the joint probability density function fXY (x, y) g(x)h( y), where g(x) is a function only of x...

The continuous random variables X and Y are jointly distributed with joint probability density function f(x, y) = kx, (0

Show that random variables X and Y are independent of the joint probability density function f(x, y) = k(4x- = k (4x = x - 2xy+1 + () (xy)). 0

A statistic question. Please help. The lifespan of a new Samsung Phone and a new Samsung Tablet are assumed to b (a) continuous and (b) respectively uniformly distributed in [3, 7] and [3, 8]. Let's...

answer File Preview 5. Suppose the cumulative distribution function of a continuous random variable X is given by 0, x1 Find the probability density function of X (note: you may assume that the...

Let X and Y be two independent and identically distributed standard normal random variables. Let # 6 0. 2x), U and V be two random variables such that: U = X cos0 - Y sind V = X sine + Y cose Show...

7 Let U1 and U2 be two independent random variables, both uniformly distributed over [0, a]. Let V = min{U1, U2} and Z = max{U1, U2}. Show that the joint distribution function of V and Z is given by...

ATel Electronics, Inc.s accounting data show the following balances for 2013 and 2014: The accountant also provided the following additional information: 1. ATel Electronics uses the perpetual...

The range of electromagnetic wave frequencies on the FM radio band is 88.0 MHz to 108 MHz (a) What is the range of wavelengths for the FM radio band? (b) What is the range of photon energy for the FM...

14.9 A company buys its annual requirement of 36,000 units in six instalments. Each unit costs fl and the ordering cost is n5. The inventory carrying cost is estimated at 20% of unit value. Find the...

2. If individuals remove funds from their checkable deposits and transfer them to their money market accounts, will M1 fall and M2 rise? Explain your answer.

What is the estimated rate of increase in bone density of the lumbar spine per year? What is the standard error of the estimated rate of increase per year? Endocrinology A 65-year-old woman with low...

Provide a significance test to assess whether the mean bone density has changed significantly over time. Provide a two-tailed p-value? Endocrinology A 65-year-old woman with low bone density in 2002...

The normal change in bone density over time from age 40 to age 80 is a decrease of 0.15 g/cm 2 . Does the rate of change in this woman differ significantly from the expected age-related change?...

Can you help me solve this statistics problem Question 17 52% of all the town's residents own a dog and 65% own a cat. Of the dog owners 45% also own a cat. If a 365 town resident is chosen at random...

In doing a five-year analysis of future dividends, the Dawson Corporation is considering the following two plans. The values represent dividends per share. Use Appendix B for an approximate answer...

If the mean of five values is9.2 and four of the values are6, 9, 14, and8, find the fifth value. The fifth value is______.