Rosa Walters is considering investing $10,000 in two mutual funds. The anticipated returns from price appreciation and dividends (in hundreds of dollars) are described by the following probability distributions. Mutual Fund A Returns Probability −2 0.3 8 0.4 10 0.3 Mutual Fund B Returns Probability −2 0.4 7 0.3 8 0.3 (a) Compute the mean and variance for Mutual Fund A. mean __ dollars variance __ dollars2
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Rosa Walters is considering investing $10,000 in two mutual funds. The anticipated returns from price appreciation and dividends (in hundreds of dollars) are described by the following probability distributions.
| Returns | Probability |
|---|---|
|
−2
|
0.3 |
|
8
|
0.4 |
|
10
|
0.3 |
Mutual Fund B
| Returns | Probability |
|---|---|
|
−2
|
0.4 |
|
7
|
0.3 |
|
8
|
0.3 |
| mean | __ dollars |
| variance | __ dollars2 |
Compute the mean and variance for Mutual Fund B.
| mean | dollars |
| variance | dollars2 |
(b) Which investment would provide Rosa with the highest expected return (the greater mean)?
(c) Which investment has the lesser element of risk (that is, which probability distribution has the smaller variance)?
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