p.313, #7

Consider a sequence of independent Bernoulli trials, each with success probability p. Let X1 be the number of failures preceding the first success, and let X2 be the number of failures between the first two successes. Find the joint density of <X1, X2>. (Note: X1 and X2 are called "waiting times")


P.315, #21

Let f(x,y) = 24xy on for (x,y) in the set
S = {(x,y)| 0<=x<=1, 0<=y<=1, 0<= x+y<=1},
and f(x,y)=0 otherwise.
1) Find the marginal density fy(y).

I was thinking integral(f(x,y),dx,0,1-y)) bt doesn't seem right. (12y^3-24y^2+12y) The answer should satisfy that integral of f from -inf to inf should be 1. Right?


2) Find E[Y]

integral(f(x,y),dx,0,1-y), then you should get 12y^3-24y^2+12y. and take integral(12y^3-24y^2+12y, dy, 0, 1), you will get 1. There is a double integral here to satisfy your statement "The answer should satisfy that integral of f from -inf to inf should be 1". I hope that helps.

i am using 5th edition:

hi, i was looking at the same question, but you said find the joint density function, it actually says joint mass function (in my version) implying that it is discrete cases, not continuous(unless updated in your version).

so as far as i know, we need to use geometric distribution with parameter P for both X and Y.

but i am stuck from there onwards.
help please

GGunit