Hi members, Show that $E[X^4]=[24]/[\lambda^4]$ When X is an exponential random variable with rate $\lambda $
Last edited by Vinod; Aug 17th 2014 at 02:55 AM.
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You can do this using the moment generating function. $M(t)=E[e^{t X}]$ $E[X^4]=\dfrac {d^4M(t)}{{dt^4}}|_{t=0}$ I leave the details to you.
Or you can use the basic definition: $\displaystyle E(X^4)= \int x^4 P(x)dx$ where P(x) is the probability density.
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