# Homework Help: Random process of uniform- graphing and pdf

1. Nov 28, 2013

### cutesteph

1. The problem statement, all variables and given/known data

Word for word of the problem:
Let N (t, a) = At be a random process and A is the uniform continuous distribution (0, 3).

(i) Sketch N(t, 1) and N(t, 2) as sample functions of t.

(ii) Find the PDF of N(2, a) = 2A.

2. Relevant equations
A pdf is 1/3 for x in [0,3]

3. The attempt at a solution

This question is very vague to me. I am not sure where to start.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Nov 28, 2013

### Ray Vickson

You have both a and A; which one do you mean?

3. Nov 28, 2013

### haruspex

I'm not familiar with this notation and terminology. I think it's saying that at time t you take a random sample x from A and get xt as the value of N. Is that right? I can only suppose that 'a' represents the random sample value, but that is strange notation since it is a function of t. Anyway, that leads to interpreting N(t, 1) as being the function of time you would get if the sample from A is always the value 1.
Correspondingly, N(2, a) is the r.v. obtained by taking samples from A and doubling them.
Does that all make sense?

4. Nov 28, 2013

### Ray Vickson

My guess would be that this type of "random process" is hardly what we usually mean by that terminology: I guess we first choose a random realization 'a' of the random variable A, then for all time we have N(t,a) = a*t. That amounts to choosing a random slope for a line, but from then on having a deterministic line. Or so, that is what I read into the problem.

5. Nov 28, 2013

### haruspex

Yes, I think that comes to the same as what I wrote, but better expressed.

6. Nov 28, 2013

### cutesteph

That makes sense now.