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Conditional Density Function on Underlying Exponential

Problem Statement: Suppose $Y_1, Y_2,\dots, Y_n$ are a random sample from an exponential distribution with mean $\theta.$ Let $\displaystyle U=\sum_{i=1}^n Y_i.$ Find the conditional density function ...
Adrian Keister's user avatar
1 vote
0 answers
54 views

joint and conditional density function

Let $f(x,y,z)$ be the joint density function. I found a reference that this joint density can be written as $f(x,y,z) = f_1(x|y,z)f_2(y|z)f_3(z)$ I'm wondering if there are alternative forms to ...
user0131's user avatar
  • 387
1 vote
0 answers
536 views

Changing a conditional probability to a deterministic function

Suppose that we have a conditional density function $p(y|x;\theta^*)$, where $\theta^*$ represents distribution parameters and are assumed to be deterministic. Is it possible that we write this ...
KRL's user avatar
  • 286
3 votes
1 answer
785 views

pdf from a set of conditional pdfs

I have an interesting problem, i have seen in many text books ways of calculating conditional pdfs but not many where given a set of conditional pdfs for a variable we wish to calculate it's pdf. In ...
Iltl's user avatar
  • 477