Problems 12. The joint density of X and Y is given by (6+x)-* otherwise f(x,y) 3D (a) Compute the density of X. (b) Compute the density of Y. (c) Are X and Y independent? 13. The joint density of X and Y is f(x,y) = 0 otherwise (a) Compute the density of X. (b) Compute the density of Y. (c) Are X and Y independent? 14. If the joint density function of X and Y factors into one part depending only on x and one depending only on y, show that X and Y are independent. That is, if show that X and Y are independent. 15. Is Problem 14 consistent with the results of Problems 12 and 13? 16. Suppose that X and Y are independent continuous random variables. Show that (a) PIX+Ys a) = 4Oy(->>-J (b) PLX S Y} p (6)YOL = where fy is the density function of Y, and Fx is the distribution functi 17. When a current / (measured in amperes) flows through a resistance R (meas in ohms), the power generated (measured in watts) is given by W R. Sup that / and R are independent random variables with densities 15850 (X-1Da9 (x)4 Ex50 %3D(x)Y Determine the density function of W.

Problems 12. The joint density of X and Y is given by (6+x)-* otherwise f(x,y) 3D (a) Compute the density of X. (b) Compute the density of Y. (c) Are X and Y independent? 13. The joint density of X and Y is f(x,y) = 0 otherwise (a) Compute the density of X. (b) Compute the density of Y. (c) Are X and Y independent? 14. If the joint density function of X and Y factors into one part depending only on x and one depending only on y, show that X and Y are independent. That is, if show that X and Y are independent. 15. Is Problem 14 consistent with the results of Problems 12 and 13? 16. Suppose that X and Y are independent continuous random variables. Show that (a) PIX+Ys a) = 4Oy(->>-J (b) PLX S Y} p (6)YOL = where fy is the density function of Y, and Fx is the distribution functi 17. When a current / (measured in amperes) flows through a resistance R (meas in ohms), the power generated (measured in watts) is given by W R. Sup that / and R are independent random variables with densities 15850 (X-1Da9 (x)4 Ex50 %3D(x)Y Determine the density function of W.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Q 13

Problems
12. The joint density of X and Y is given by
(6+x)-*
otherwise
f(x,y) 3D
(a) Compute the density of X.
(b) Compute the density of Y.
(c) Are X and Y independent?
13. The joint density of X and Y is
f(x,y) =
0 otherwise
(a) Compute the density of X.
(b) Compute the density of Y.
(c) Are X and Y independent?
14. If the joint density function of X and Y factors into one part depending only
on x and one depending only on y, show that X and Y are independent.
That is, if
show that X and Y are independent.
15. Is Problem 14 consistent with the results of Problems 12 and 13?
16. Suppose that X and Y are independent continuous random variables. Show
that
(a) PIX+Ys a) =
4Oy(->>-J
(b) PLX S Y}
p (6)YOL =
where fy is the density function of Y, and Fx is the distribution functi
17. When a current / (measured in amperes) flows through a resistance R (meas
in ohms), the power generated (measured in watts) is given by W R. Sup
that / and R are independent random variables with densities
15850 (X-1Da9 (x)4
Ex50 %3D(x)Y
Determine the density function of W.

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