In this activity, we investigate the sampling distribution of the sample mean, X 1. Imagine that you roll a single, fair, six-sided die once. Define the random variable X, to be the number of dots (pips) on the upward face. Complete the probability distribution table for X. P(x) 1 3 4. 5 2. Sketch the probability histogram for X below. Let the x-axis be the OUTCOME and let the y-axis be the PROBABILITY. 3. Determine the mean and standard deviation for X. As a reminder, you determine the mean of a discrete probability distribution using u=ExP(x) and the standard deviation is found most simply using the formula o = \E×²P(x)– µ² (see page 322).

In this activity, we investigate the sampling distribution of the sample mean, X 1. Imagine that you roll a single, fair, six-sided die once. Define the random variable X, to be the number of dots (pips) on the upward face. Complete the probability distribution table for X. P(x) 1 3 4. 5 2. Sketch the probability histogram for X below. Let the x-axis be the OUTCOME and let the y-axis be the PROBABILITY. 3. Determine the mean and standard deviation for X. As a reminder, you determine the mean of a discrete probability distribution using u=ExP(x) and the standard deviation is found most simply using the formula o = \E×²P(x)– µ² (see page 322).

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Description: In this activity, we investigate the sampling distribution of the sample mean, $\bar{X}$.### 1. Probability DistributionImagine that you roll a single, fair, six-sided die once. Define the random variable $X$ to be the number of dots (pips) on t

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Topic Video

Question

In this activity, we investigate the sampling distribution of the sample mean, $\bar{X}$.

### 1. Probability Distribution

Imagine that you roll a single, fair, six-sided die once. Define the random variable $X$ to be the number of dots (pips) on the upward face. Complete the probability distribution table for $X$.

| x | P(x) |
|---|------|
| 0 | |
| 1 | |
| 2 | |
| 3 | |
| 4 | |
| 5 | |
| 6 | |

### 2. Histogram

Sketch the probability histogram for $X$ below. Let the x-axis be the OUTCOME and let the y-axis be the PROBABILITY.

(Blank graph for sketching with labeled axes, x-axis labeled "Outcome" and y-axis labeled "Probability")

### 3. Mean and Standard Deviation

Determine the mean and standard deviation for $X$. As a reminder, you determine the mean of a discrete probability distribution using:

\[
\mu = \sum xP(x)
\]

and the standard deviation is found most simply using the formula:

\[
\sigma = \sqrt{\sum x^2P(x) - \mu^2}
\]

(see page 322).

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