Consider the Given Discrete Probability Distribution $\begin{array}{|c|c|c|c|c|c|}\hline x & 1 & 2 & 3 & 4 & 5 \\\hline p(x) & .1 & .2 & .2 & .3 & .2 \\\hline\end{array}$

question 49

Essay

Consider the given discrete probability distribution. $\begin{array}{|c|c|c|c|c|c|}\hline x & 1 & 2 & 3 & 4 & 5 \\\hline p(x) & .1 & .2 & .2 & .3 & .2 \\\hline\end{array}$

a. Find $\mu = E ( x )$ .
b. Find $\sigma = \sqrt { E \left[ ( x - \mu ) ^ { 2 } \right] }$ .
c. Find the probability that the value of $x$ falls within one standard deviation of the mean. Compare this result to the Empirical Rule.

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Definitions:

Maturity Value

The total amount payable to an investor at the end of a security's hold period, including both the principal and interest.

Maturity Value

The total amount that will be paid to an investor at the maturity date of a financial instrument, including principal and interest.

Bank Discount

The difference between the face value of a banknote or security and its selling price, before it reaches its maturity.

Discount Period

The time frame within which a buyer can pay less than the full amount due by taking advantage of a discount offered by the seller.