Develop a model to load a dice that gets a roll of 6 50 of t

Develop a model to load a dice that gets a roll of \"6\" 50% of the rolls and has an equal chance at rolling a \"1,2,3,4 or 5\" the other 50% of the rolls. Simulate 100 rolls. provide a summary statistics and a histogram of your findings. Discuss your results.

Solution

The pmf of given problem is

X            1                  2           3              4         5                6

P(X=x)    1/10          1/10         1/10        1/10       1/10          1/2(=0.50)

The simulate the 100 samples are

The summary statistics are

Descriptive Statistics: Samples

                Total                                            Sum of
Variable Count   Mean StDev Variance CoefVar      Sum   Squares Minimum
Samples     100 4.310 1.983     3.933    46.01    431.000 2247.000    1.000

                                              N for
Variable     Q1      Median     Q3 Maximum Mode   Mode Skewness Kurtosis
Samples   2.000   5.000    6.000    6.000    6         49     -0.64     -1.27

Histogram of the samples

The shape of the histogram shows that negative skewnees. The coefficient of skewness is -0.64. It is clearly -ve skewness distribution. Mode is 6 since it occurs 49 times out of 100 observations.

Here, Mean (4.31) < Median (5) < Mode(6). This condition is related to negative skewness.