Question

Suppose you roll two twenty-five-sided dice. Let X1, X2 the outcomes of the rolls of these two fair dice which can be viewed as a random sample of size 2 from a uniform distribution on integers.

a) What is population from which these random samples are drawn? Find the mean (µ) and variance of this population (σ 2 )? Show your calculations and results.

b) List all possible samples and calculate the value of the sample mean ¯(X) and variance (s 2 ) for each sample?

c) Obtain the sampling distribution of X¯ from this list by creating a frequency distribution table. You can create a frequency distribution table using Excel and share it on your file. Then calculate relative frequencies, i.e., f(x), which give the probabilities of the sampling distribution of X¯, and calculate the mean of the sampling distribution, i.e., xf(x). Check if that equals to (µ).

d) Make a Histogram for the sampling distribution of X¯ you have obtained in (c). Use the Data Analysis Toolpak in Excel to make the Histogram. For Bins, use the Row Labels of the frequency tables you have created in (c).

e) Calculate the Skewness and Kurtosis for the sample mean ¯(X) you have obtained in (b). Explain your results. Do the Histogram in (d) and your results in (e) show any indications that the data is symmetrically distributed? Explain.

**I only need questions d and e completed**

**please complete on word file**

Answer #1

d)

(e)

Measure of skewness=0.0000

Measure of kurtosis=-0.5971

Excel output:

Column1 | |

Mean | 13 |

Standard Error | 0.204124 |

Median | 13 |

Mode | 13 |

Standard Deviation | 5.103104 |

Sample Variance | 26.04167 |

Kurtosis | -0.5971 |

Skewness | -8.6E-18 |

Range | 24 |

Minimum | 1 |

Maximum | 25 |

Sum | 8125 |

Count | 625 |

Since skewness is almost zero hence the data is symmetric and this is also observed from histogram.

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