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| Math Central | Quandaries & Queries |
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Question from Donny, a student: An investment will be worth $1,000, $2,000, or $5,000 at the end of the year. The probabilities of these values are .25, .60, and .15, respectively. Determine the mean and variance of the worth of the investment. |
Hi Donny,
To find the mean or expected value where there are only a finite number of possible outcomes you take each possible value, multiply by the probability that this outcome occurs and then add the resulting values. For your example that is
mean = $1,000 × 0.25 + $2,000 × 0.60 + $5,000 × 0.15
Once you have the mean you can find the variance as follows. Take each possible value, subtract the mean and square the result. For your example that gives you
($1,000 - mean)2, ($2,000 - mean)2 and ($5,000 - mean)2
Now take the three numbers in the line above, multiply each by the probability of obtaining the respective outcome and add the results much as you did to find the mean. This gives the variance.
I hope this helps,
Harley
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