Thread: cumulative distribution

Hi ^^

This question asks me to compute the cdf of Y from this pdf :
f(y) { y/25 for 0 =< y < 5 ; (2/5) - (y/25) for 5 =< y =< 10 ; 0 for otherwise }

After I integrate the function (because F'(x) = f(x)), I got:

F(y) { 0 for y<0 ; y^2/50 for 0 =< y < 5 ; (2y/5) - y^2/50 for 5=<y=<10 ; 1 for y => 10}
this cdf is weird because if i plug 10 in, like (2(10)/5) - (10)^2/50) i got 2 instead of 1 . I don't understand, would someone like to explain to me thank you very much ^^

You need to go back to the definition of the cdf, which is

If y<0, then F(y)=0.

If 0<y<5, then you are correct,

HOWEVER, and it's good you check your work...

If 5<y<10, then =.5 + whatever.

And, for y>10, you better get 1, which I did, since this is a valid denisty.
That was the first thing I did, to see if it integrated to one.
Too often students write down incorrect 'densities' and I spend forever on the problem.

From what I can make out from the question...



and



should sum to 1.

Mr Pickles, it is a valid density, but he's misunderstanding what a CDF is.

i see my mistake thank you very much ^^