Let X be a continuous random variable with the following p.d.f
fx(x) ax 0<=x<1
a 1<=x<2
-ax+3a 2<=x<3
0 otherwise.
Then, (a) Determine the constant, a, (b)Calculate P(X>2)? (c) If W,Y,Z are three independent observations from X, what is the probability that exact one of hese numbers is larger than 2?

I have no idea of what the problem is about. Could you try and post it in a clearer way? :confused:

Let X be a continuous random variable with the following p.d.f.


(ax 0<= x < 1
fx(x) ={a 1<= x < 2
(-ax + 3a 2<= x < 3
(0 otherwise

Then, (a) Determine the constant,
(b) Calculate P(X>2) = ?
(c) If W,Y,Z are three independent observations from X, what is the probability that exact one of these numbers is larger than 2 ?

Please Help !

Could you stick to a single account please?

And your question is still incomprehensible. Could you explain how the data given is displayed? Like... is there a table, if so, what is the column headings, what is in which column etc. If you want help, you must do your part too.

I believe this is it:

A probability density function.

f(x)=\left\{\begin{array}ax, \;\ 0\leq x<1\\ a, \;\ 1\leq x<2\\ -ax+3a, \;\ 2\leq x<3\\ 0, \;\ \text{otherwise}\end{array}


Note that probability densities sum to 1.

That is, \int_{-\infty}^{\infty}f(x)dx=1

You integrate, set to 1 and solve for a.