The lengths of the minor and major axes are used to summarize dust particles that are approximately

Question:

The lengths of the minor and major axes are used to summarize dust particles that are approximately elliptical in shape. Let X and Y denote the lengths of the minor and major axes (in micrometers), respectively. Suppose that fX (x) = exp(−x),0 < x and the conditional distribution fY|x (y) = exp[−(y − x)], x < y. Answer or determine the following:

(a) That fY|x (y) is a probability density function for any value of x.

(b) P(X < Y) and comment on the magnitudes of X and Y .

(c) Joint probability density function fXY (x, y).

(d) Conditional probability density function of X given Y = y.

(e) P(Y < 2 | X = 1) 

(f) E(Y | X = 1)

(g) P(X < 1, Y < 1) 

(h) P(Y < 2)

(i) c such that P(Y < c) = 0.9

(j) Are X and Y independent?

Distribution
The word "distribution" has several meanings in the financial world, most of them pertaining to the payment of assets from a fund, account, or individual security to an investor or beneficiary. Retirement account distributions are among the most...
Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For  book-img-for-question

Applied Statistics And Probability For Engineers

ISBN: 9781118539712

6th Edition

Authors: Douglas C. Montgomery, George C. Runger

Question Posted: