An investor is considering six different money market funds....

An investor is considering six different money market funds. The average number of days to maturity for each of these funds is as follows: $41,39,35,35,33,38$ Two of these funds are to be chosen at random. a. How many possible samples of two funds are there? b. List all possible samples. c. Find the probability function of the sampling distribution of the sample means. d. Verify directly that the mean of the sampling distribution of the sample means is equal to the population mean.

An investor is considering six different money market funds. The average number of days to maturity for each of these funds is as follows:
$41,39,35,35,33,38$
Two of these funds are to be chosen at random.
a. How many possible samples of two funds are there?
b. List all possible samples.
c. Find the probability function of the sampling distribution of the sample means.
d. Verify directly that the mean of the sampling distribution of the sample means is equal to the population mean.

Key Concepts

Combination Theory

This concept deals with counting the number of ways that items can be selected from a larger set when the order of selection does not matter. In statistics, combinations are used to determine the number of different possible samples or pairs that can be drawn from a given population, which is essential in many sampling problems and probability calculations.

Sampling Distribution of the Sample Mean

The sampling distribution of the sample mean is the probability distribution of the means obtained from all possible samples of a fixed size taken from a population. This concept is crucial for understanding how sample means relate to the overall population mean, and it forms the basis for many inferential statistical procedures and the Central Limit Theorem.

Probability Function

A probability function assigns a probability to each outcome in the sample space. In the context of sampling distributions, the probability function specifies the likelihood of obtaining each possible sample mean, allowing one to understand the distribution and spread of these means across all possible samples.

Unbiased Estimation

Unbiased estimation is a property of an estimator wherein the expected value of the estimator equals the true value of the population parameter. When verifying that the mean of the sampling distribution of the sample means is equal to the population mean, this demonstrates that the sample mean is an unbiased estimator of the population mean.

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