# 1)A rewiew of voted registration record in a small town yielded the dollowing data of the number of males and females registered as Democrat,

Modeling data distributions

1)A rewiew of voted registration record in a small town yielded the dollowing data of the number of males and females registered as Democrat, Republican, or some other affilation:

$$\begin{array}{c} Gender \\ \hline Affilation & Male & Female \\ \hline Democrat & 300 & 600 \\ Republican & 500 & 300 \\ Other & 200 & 100 \\ \hline \end{array}$$

What proportion of all voters is male and registered as a Democrat? 2)A survey was conducted invocted involving 303 subject concerning their preferences with respect to the size of car thay would consider purchasing. The following table shows the count of the responses by gender of the respondents:

$$\begin{array}{c} Size\ of\ Car \\ \hline Gender & Small & Medium & lange & Total \\ \hline Female & 58 & 63 & 17 & 138 \\ Male & 79 & 61 & 25 & 165 \\ Total & 137 & 124 & 42 & 303 \\ \hline \end{array}$$

the data are to be summarized by constructing marginal distributions. In the marginal distributio for car size, the entry for mediums car is ?

2020-11-08

1) Given data table , $$\begin{array}{|c|c|} \hline Gender \\ \hline Affiliation & Male & Female & Total \\ \hline Democrat & 300 & 600 & 900 \\ \hline Republican & 500 & 300 & 800 \\ \hline Other & 200 & 100 & 300 \\\hline Total & 1000 & 1000 & 2000 \\ \hline \end{array}$$ Number of all voters male and registered as a democrat x = 300 Total voters = n = 2000 Proportion of all voters is male and registered as democrat is , $$\frac{x}{n} = \frac{300}{2000} = 0.15$$

2) Given data table, $$\begin{array}{c} Size\ of\ Car \\ \hline Gender & Small & Medium & lange & Total \\ \hline Female & 58 & 63 & 17 & 138 \\ Male & 79 & 61 & 25 & 165 \\ Total & 137 & 124 & 42 & 303 \\ \hline \end{array}$$ The marginal distribution of car size, $$\begin{array}{|c|c|} \hline Size\ of\ car & small & medium & large & total \\ \hline Probability & \frac{137}{303} = 0.452 & \frac{124}{303} = 0.409 & \frac{42}{303} = 0.137 & 1\\ \hline \end{array}$$ In the marginal distribution for car size, the entry for medium cars is 0.409