Consider the Population Described by the Probability Distribution Below $\begin{array}{c|c|c|c}x & 3 & 5 & 7 \\\hline p(x) & .1 & .7 & .2\end{array}$

question 1

Essay

Consider the population described by the probability distribution below. $\begin{array}{c|c|c|c}x & 3 & 5 & 7 \\\hline p(x) & .1 & .7 & .2\end{array}$

a. Find $\mu$ .
b. Find the sampling distribution of the sample median for a random sample of $n = 2$ observations from this population.
c. Show that the median is an unbiased estimator of $\mu$ .

Understand the process of calculating chi-square statistics for given data.

Apply decision rules for hypothesis testing based on chi-square statistics.

Calculate expected frequencies for categories within datasets.

Understand and apply the concept of degrees of freedom in the context of chi-square tests.

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Definitions:

Call Provisions

Terms in a bond contract that allow the issuer to repurchase and retire the bond at a specified price before maturity, protecting against interest rate risk.

Bond Indenture

A legal contract between a bond issuer and a bondholder, detailing the terms of the bond such as the coupon rate, maturity date, and obligations of the issuer.

Call Provision

A clause in a bond or other fixed-income security that allows the issuer to repay the principal before the maturity date.

Sinking Fund

A savings fund into which an organization sets aside money over time, intended to pay off a debt or bond at its maturity or to meet a future capital expense.