2
votes
2answers
40 views

Density of sum of two uniform random variables

I have two uniform random varibles. $X$ is uniform over $[\frac{1}{2},1]$ and $Y$ is uniform over $[0,1]$. I want to find the density funciton for $Z=X+Y$. There are many solutions to this on this ...
0
votes
0answers
11 views

convolution of 3 uniform random variables

Please help. X,Y,Z are uniformly distributed random variates over the closed interval [3,5] independently/ The sum, S, of any of the two random variates X,Y,Z has a triangular distribution with pdf: ...
1
vote
3answers
62 views

Convolution of maximum and minimum of uniform random variables

Let $X_1,\ldots, X_n$ be $n$ independent random variables uniformly distributed on $[0,1]$. Let be $Y=\min(X_i)$ and $Z=\max(X_i) $. Calculate the cdf of $(Y,Z)$ and verify $(Y,Z)$ has independent ...
1
vote
1answer
55 views

What is the distribution of $X+Y$ where $X \sim U(0,\frac{L}{2})$ and $Y \sim U(\frac{L}{2},L)$?

I started along these lines: Let $Z = X + Y$ where $\frac{L}{2}< z < \frac{3L}{2}$, then, $$f_{X+Y}(z)=f_{Z}(z) = \int f_{X}(x)f_{Y}(z-x)dx$$ However, I am not sure how to fill in the bounds ...
-2
votes
1answer
168 views

Convolution of Discrete Uniform ,$DU$, Distribution.

If $X\sim DU(k,a,h),\quad -\infty<a<\infty,h>0=1,2,\ldots$ then the probability function is $$P(X=a+jh)=\frac{1}{k},\quad j=0,1,\ldots,k-1$$ Let $Z\sim DU(r,0,s)$ and $Y\sim DU(s,0,1)$ , ...
1
vote
2answers
897 views

Sum of random variables uniformly distributed (0,1) and (0,2)

I'm trying to get $P(0.9<Y<=1.8)$ for the sum of 2 random and uniform values x1,x2 (so that y=x1+x2) where $x1$~$u(0,1)$ and $x2$~$(0,2)$ and I'm trying to do the convolution for it. Seems like ...
3
votes
1answer
146 views

Estimating number drawn from one distribution based on sum of that number and number drawn from another distribution

I have been working on this for several days and have been unable to come up with an answer. The problem is very simple to state, but it seems difficult to solve. A computer draws a number $x$ at ...