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Simple series problem

  1. Sep 10, 2007 #1
    Find [tex] \mu_1 ^' \mobx{ and } \mu_2^' \\[/tex] the first and second moments about the origin, of the probability function p(x) = 1 ( 0<= x <= 1). Show that the value of [tex] M(a)= \int_0^1 exp{ax}\ dx \mbox{ is }\frac{1}{a}(exp{a}-1) [/tex]. Expand M(a) in a series of ascending powers of a and show that the coefficients of a and [tex] \frac{a^2}{2!} [/tex] in this expansion are equal to values [tex] \mu_1 ^' \ \mbox{ and }\ \mu_2 ^' \\ \ \mbox{ I get } \ \mu_1 ^' \ = \frac{1}{2}\ \mbox{ and }\ \mu_2 ^'\ = \frac{1}{3} [/tex], and I get M(a) equal to what it says, from which I get M(0)=0, M'(0)=1 not 1/2 and I get M''(0)=-1 and not 2/3. I assume it is a Maclaurin's series that is the series required.Thanks for helping.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
    Last edited: Sep 10, 2007
  2. jcsd
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