Here's a question:
Let X have a continuous uniform distribution on the interval [a,b]. Find the density function for this dristribution and then verify that and .
So here's what I "think" I should do ...
Let f(x) = 1/(b-a) = 1 assuming that a=0 and b=1
For a <= x <= b
I know I need to integrate, but I'm not sure how to set up the problem
where f(x) = 1
which equals 1/2 when pluging in [a.b]
and then we have
When you plug in the interval [0,1] you get
verifying You also get
Is this correct? wow, that was long, sorry, I just tried to do it myself without any help at first. Be nice to me, it's my first post and it's also my birthday! WOOHOO
Thanks for all the help
Here is my birthday present to you, TaoWine:
The pdf of X is for and zero elsewhere.
By symmetry this expectation is totally expected .
I leave you to find:
X has a continuous uniform distribution on the interval [a,b]
Means that the pdf of is a constant on and zero everywhere else. So let the pdf of be:
To be a pdf we require that the integral of this over be . So: