Let X be a normal random variable with mean m X and variance 2 X .
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Let X be a normal random variable with mean mX and variance σ2X. Show that the higher central moments of the normal random variable are given by
![E[(X -mx)"]= 0, {} (n-1)(n-3).3. 10x, n odd n even.](https://dsd5zvtm8ll6.cloudfront.net/images/question_images/1700/4/6/4/827655b08bb232421700464826205.jpg)
For the log-normal random variable Z = exp(αX), α is a real constant, show that
![E[Z] = exp amx+ p(amx a -0).](https://dsd5zvtm8ll6.cloudfront.net/images/question_images/1700/4/6/4/853655b08d5963711700464852703.jpg)
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