SOLUTION: Probability Density. HELP PLEASE !!!! A broom stick of length 1 meter is split into two substicks at a point that is uniformly distributed. Let X be the length of the shorter subs

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Question 287629: Probability Density. HELP PLEASE !!!!
A broom stick of length 1 meter is split into two substicks at a point that is uniformly distributed. Let X be the length of the shorter substick and Y be the length of the longer substick.
Find
(a) the density of X
(b) the density of Y
(c) E(X)
(d) Var(X)
(e) E(Y - X)2
As no one is attempting to answer this question (that I have posted several times), can I assume it's unsolvable ?
Someone PLEASE reply !!!!
Found 2 solutions by richwmiller, robertb:
Answer by richwmiller(17219) (Show Source):
You can put this solution on YOUR website!
You can assume that we don't appreciate your whining. Attempting to belittle the tutors will get you nowhere.
Not every problem gets solved but the percentages are high.
Some reasons problems don't get solved:
1-The problem is written so poorly that we can't understand your writing.
( That could include missing data, unclear instructions)
2- There have been a mess of similar problems lately sometimes by the same people.
3. The problem is not interesting.
4- The problem is involved and there are other problems to do.
[Why spend 30 minutes on one problem when I could help 30 others in the same time.]
5-We seem to be inundated by probability problems lately and the focus of this website is algebra.
6-There aren't many tutors who work on probability and statistics problems.
7- Attitude of entitlement by the student. No one is entitled to an answer. The volunteers are just that- volunteers. There are other poor attitudes including whining was already mentioned.
8- Along with attitude comes your participation. We are here to teach not do your homework. So where is your attempt to solve the problem? What have you tried? What do you see as the approach to the problem?

Answer by robertb(5830) (Show Source):
You can put this solution on YOUR website!
f(x) = 1, x in [0,1],
f(y) = 1, y in [0,1]. (Here, Y = 1 - X.)

Now
<==> .
var(Y-X) = varY + varX = var(1-X) + var X = var 1 + var X + var X = 2var X = 2/12 = 1/6.
E(Y - X) = E(Y) - E(X) = E(1 - X) - E(X) = E1 - E(X) - E(X) = 1 - 2E(X) =
1 - 1 = 0.
==>