Value & Probability $1000 - .25; $2000 .60 & $5000 .15. What is the mean & variance?

Question

An investment will be worth $1000, $2000 or $5000 at the end of the year. The probabilities are .25, .60, and .15, respectively. What is the mean and what is the variance?

Answer 1

Dear Debra S,

The mean is a weighted average of the possible payouts, where the weights are the respective probabilities. Thus, for this question,

mean = (0.25 x $1000) + (0.60 x $2000) + (0.15 x $5000)
= $250 + $1200 + $750
= $2200 .

For the variance, you square the difference between each possible payout and the mean (which we just calculated above), then use the same weights (i.e., the probabilities) to form a weighted average of these squared differences. So for this question,

variance = (0.25 x [$1000 - $2200]^2) + (0.60 x [$2000-$2200]^2)
+ (0.15 x [$5000 - $2200]^2)
= (0.25 x [-$1200]^2) + (0.60 x [-$200]^2) + (0.15 x [$2800]^2)
= (0.25 x 1440000) + (0.60 x 40000) + (0.15 x 7840000)
= 360000 + 24000 + 1176000
= 1560000 (the units are in "$ squared").

Answer 2

I do not now