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 ZMD October 6th, 2017 04:14 PM

Expected Value

X is a random variable over [1,2]
1. Find distribution function of Y=e$^x$
2. Find E[Y] i.e expected value of Y

I'm done with part a. The answer is 1/y .
Can anyone help calculate the expected value.

 romsek October 6th, 2017 04:43 PM

The answer to part a is not $\dfrac 1 y$

It is $f_Y(y) = \begin{cases}0 & y < e \\ \dfrac 1 y &y \in [e,e^2] \\ 0 &e^2 < y \end{cases}$

There is a serious difference.

$E[Y] = \displaystyle \int_e^{e^2}~y\dfrac 1 y~dy = \int_e^{e^2}~1=e^2-e$

 Country Boy October 8th, 2017 03:46 AM

Romsek is assuming you meant "x is uniformly distributed over [1, 2]". Just saying "x is a random variable over [1, 2]" does not tell us the probability distribution which is necessary in order to answer this question.

 romsek October 8th, 2017 09:40 AM

Quote:
 Originally Posted by Country Boy (Post 581732) Romsek is assuming you meant "x is uniformly distributed over [1, 2]". Just saying "x is a random variable over [1, 2]" does not tell us the probability distribution which is necessary in order to answer this question.
Yeah. It's fairly a given that if they don't mention some other distribution they mean uniform if it's over a closed interval.

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