Question

Refer to the probability distribution displayed in Table \(5.11\) on page \(222\).

a. Use the technology of your choice to repeat the simulation done in Example \(5.18\) on page \(223\).

b. Obtain the proportions for the number of heads in three tosses and compare them to the probability distribution in Table \(5.11\).

c. Obtain a histogram of the proportions and compare it to the probability histogram in Fig. \(5.22\)(b) on page \(223\).

d. What do part (b) and (c) illustrate?

Short answer

Part a.

Part b. As we can see in the table the proportions are slightly differ from the probability, but they do not differ very much.

Part c.

Part d. From part b and c, we can say that the different sample leads to different estimated probabilities and a different probability histogram.

Step-by-step solution

Part a. Step 1. Given information

The number of games is given.

Part a. Step 2. Calculation

Using the MATLAB sketch, a bar graph between proportion and number of heads because number of proportions is probability of heads will come.

Program:

clc

clear

closeall

\(x=[0 1 2 3]\);

\(y=[0.136 0.377 0.368 0.119]\);

\(bar(x,y)\)

\(set(gca,'linewidth',1.2,'fontsize',12)\)

\(xlabel('Number of heads')\)

\(ylabel('Proportion')\)

axis square

Query:

• First, we have defined the number of heads.
• Then define the proportion.

• Sketch a graph using function “bar”

Part b. Step 1. Calculation

Using the MATLAB sketch, a bar graph between proportion and number of heads because number of proportions is probability of heads will come.

Show the comparison between both tables.

Part c. Step 1. Calculation

Using the MATLAB sketch, a bar graph between proportion and number of heads because number of proportions is probability of heads will come.

Show the comparison between both tables.

Program:

clc

clear

closeall

\(x=[0 1 2 3]\);

\(y=[0.136 0.377 0.368 0.119]\);

\(p=[0.125 0.375 0.375 0.125]\);

\(subplot(1,2,1)\)

\(bar(x,y)\)

\(set(gca,'linewidth',1.2,'fontsize',12)\)

\(xlabel('Number of heads')\)

\(ylabel('Proportion')\)

axis square

\(subplot(1,2,2)\)

bar(x,p)

\(set(gca,'linewidth',1.2,'fontsize',12)\)

xlabel('Number of heads')

ylabel('probabilty')

axis square

Query:

• First, we have defined the number of heads.
• Then define the proportion.
• Sketch a graph using function “bar”
• Show the comparison between proportion and probability.

Part d. Step 1. Calculation

From part b and c, we can say that the different sample leads to different estimated probabilities and a different probability histogram.