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I'm trying to determine the total expected gain or loss over a one year period given an investment that has the following probabilities (over the same one year period):

$P($2000 loss) = .25

$P($1000 profit) = .2

$P($5000 profit) = .15

$P($0 profit) = .4

My approach is as follows:

$P($loss) = .25(-2000) = - 500

$P($gain) = .2(1000)+.15(5000)+.4(0) = 950

Expected gain/loss = gain - loss

Expected gain/loss = 950 - 500 = $450

I feel like i'm missing something critical here, mostly pertaining to the 40% probability of breaking even.

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  • $\begingroup$ What is the result of $0.2(1000)+.15(5000)+.4(0)$ ? Please calculate it again. $\endgroup$ – callculus Oct 31 '15 at 18:31
  • $\begingroup$ $-2000\cdot0.25+1000\cdot0.2+5000\cdot0.15+0\cdot0.4=450$ $\endgroup$ – barak manos Oct 31 '15 at 18:33
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The best way to formulate this :

Let $X$ be a random variable with

$P(X = -2000) = 0.25$

$P(X=1000) = 0.2$

$P(X = 5000) = 0.15$

$P(X = 0) = 0.4$

Then, $E(X)=(-2000)\times 0.25+1000\times0.2 +5000\times 0.15+0\times 0.4=450$

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    $\begingroup$ Thanks Peter, this is a much more clear and concise way to look at the problem. $\endgroup$ – JTW Oct 31 '15 at 18:37

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