In considering the purchase of a certain stock, you attach...

In considering the purchase of a certain stock, you attach the following probabilities to possible changes in the stock price over the next year. Stock Price Change During Next Twelve Months (%) Probability +15 0.2 +5 0.3 0 0.4 -5 0.05 -15 0.05 What is the expected value, the variance, and the standard deviation? Which is the most likely outcome?

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00:01 In this table, we are given the probability distribution for the change in the price of a stock over the next year.

00:09 And we are asked for the expected value, the variance, standard deviation, and the most likely outcome.

00:17 So this is a discrete random variable.

00:19 For any discrete random variable, let's call this x, this change.

00:25 We'll just label it as a random variable x.

00:27 For any discrete random variable, the expected value is given by the...

00:34 Formula.

00:35 It's the summation over all possible values of the random variable of x times the probability of x.

00:47 So for this situation that is 15 times 0 .2 plus 5 times 0 .3 and so on.

01:18 And this comes out to 3 .5.

01:21 So the expected value or the expected percent change in the stock over the next 12 months is 3 .5 percent.

01:31 Now for the variance, for discrete random variable, the variance is given by this formula.

01:40 Again, it's the summation over all possible values of x of x minus the mean squared times the probability of x.

01:53 Now the mean is the expected value, so this is the mean.

01:58 This formula can also be rewritten like this, which is a little bit easier to compute sometimes.

02:09 So let's use this formula for computing this...

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