Math Problem Statement

The expected value for the probability distribution used, a uniform discrete distribution, is calculated in Table 2 below as E(x) = m = 18.5. What is the point estimate, x̅, for m as calculated from the actual selection data through October 9, 2024 in Table 1?

Solution

The point estimate xˉ\bar{x} for the population mean mm is calculated as the sample mean from the actual selection data in Table 1. To find xˉ\bar{x}, you need to sum up all the values in Table 1 and divide by the total number of observations in that table.

Here’s the general formula for calculating xˉ\bar{x}:

xˉ=1ni=1nxi\bar{x} = \frac{1}{n} \sum_{i=1}^{n} x_i

Where:

  • nn is the total number of data points (sample size).
  • xix_i are the individual values in the sample (the data from Table 1).

You would:

  1. Add up all the values from Table 1.
  2. Divide the sum by the total number of values (the sample size) to obtain xˉ\bar{x}, the sample mean or point estimate of mm.

If you can provide the values from Table 1, I can help you calculate xˉ\bar{x}.

Do you have the data from Table 1, or would you like to clarify further?


Would you like details on how to compute expected value and sample mean from tables? Here are 5 questions that expand on this concept:

  1. How does the sample mean xˉ\bar{x} relate to the population mean mm?
  2. What is the difference between a point estimate and an interval estimate?
  3. Why is the expected value important in probability distributions?
  4. Can we assume that the sample mean xˉ\bar{x} will always equal the population mean mm?
  5. What factors might cause discrepancies between the sample mean and the expected value?

Tip: When working with large data sets, it's useful to organize the data in a table or spreadsheet to compute sums and averages quickly.

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Math Problem Analysis

Mathematical Concepts

Statistics
Probability Distributions
Point Estimates
Sample Mean

Formulas

Sample mean formula: \( \bar{x} = \frac{1}{n} \sum_{i=1}^{n} x_i \)

Theorems

Law of Large Numbers
Central Limit Theorem

Suitable Grade Level

College Level (Introductory Statistics)