Is the Moment Generating Function Solution Correct?

boneill3
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Homework Statement



Find the mgf of 2/25*(5-y) fo 0<y<5

Homework Equations



M(t) = INT e^yt f(y)dy

The Attempt at a Solution



= (2*(e^(5t)-5t-1))/25t

Is this ok
 
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I got a different denominator. One of us is wrong, probably me?
 
Sorry my mistake I forgot to square the denomiator Is this better?

= (2*(e^(5t)-5t-1))/(25t)^2
regards
Brendan
 
25 shouldn't be squared.
 
Oops
= (2*(e^(5t)-5t-1))/25t^2
Brendan
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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