In This Section, We Illustrate the Use of JMP for Computing Various Probabilities

In This Section, We Illustrate the Use of JMP for Computing Various Probabilities

4.12 Using JMP

In this section, we illustrate the use of JMP for computing various probabilities.

Note: the statistical packages discussed in this book use p to denote the probability of success, whereas we have used.

Example 4.12.1 (Using JMP) Refer to Example 4.4.1. Find the probabilities of getting x = 0, 1, 2, 3, … , 13 spades in a hand of bridge.

Solution:In order to determine the probability P(), where X is distributed by the hypergeometric distribution with sample space x = 0, 1, 2 ,…, 13 using JMP, proceed as follows:

  1. From the main JMP taskbar, select FileNew Data Table, which results in an Untitled new data table in a separate screen. To change “Untitled” to another title, point the cursor to the “Untitled” box in the left top corner, right click twice, and enter the new title.

2. Create 2 columns, Column 1 and Column 2, in a New Data Table.

3. Enter the values 0, 1, 2, …, 13 in Column 1.

4. Label Column 2 as H(52, 13,13) and right-click on H(52, 13,13). Then select Formula option. Another dialog box H(52, 13,13) appears.

5. In the dialog box H(52, 13,13), select Probability option from the Function (grouped). Scroll down the menu and select the Hypergeometric Probability (for cumulative probabilities select Hypergeometric Distribution option).

6. In the text box below Hypergeometric Probability, [[N] [K] [n] [x]] will show up in Text box. Enter the value 52 for N, 13 for K(=),13for n, and select Column 1 from the Table Columns, which will appear within the parentheses, for x.

7. Select Apply to have the probability values appear in Column 2, as shown below.

Example 4.12.2 (Using JMP) Refer to Example 4.6.2. Find the probability that x number of ninesoccur, where x = 0, 1, 2 ,…, 100.

Solution: In order to determine the probabilities, where X is the binomial random variable with and where x = 0, 1, 2 ,…, 100 using JMP, proceed as follows:

1. In the JMP starter dialog box click New Data Table;then an Untitled new dialog box appears. To rename the data table,place the cursor onthe box labeled “Untitled” in the left corner,single- click the entry, and enter the desired title.

2. Create 2 columns, Column 1 and Column 2, in a New Data Table.

3. Enter the values 0, 1, 2, …, 100 in Column 1.

4. Label Column 2 as B(100,.111) and right-click on B(100, .111). Thenselect the Formula option.Another dialog box B(100,.111) appears,

  1. In the dialog box B(100,.111), select DiscreteProbability option from the Functions (grouped). Scroll

down the menu and select the Binomial Probability (for cumulative probabilities select Binomial Distribution option),

  1. In the text box below,Binomial Probability, [[p] [n] [x]] will show up. Enter the

value .111 for p, 100 for n, and select Column 1 from the Table Columns,which will appear within the parenthesis, for x,and

  1. Select Apply to have the probability values appear in Column 2, as shown below.

Example 4.12.3 (Using JMP) A manufacturing companyof car parts found that one of its machines produces defective parts at random. Further, the company determined that X, the number of defective parts this machine produces in each shift is distributed as a Poisson distribution with = 3. Find the probability that the machine will produce x number of defective parts in the next two shifts, where x = 0, 1, 2, …, 10, 11, or 12.

Solution: From Equation (4.8.1), it follows that X, the number of defective parts the machine will produce in two shifts, is distributed as a Poisson distribution with = 6. To find the probabilities, x = 0, 1, 2, …, 10, 11, or 12 using JMP, proceed as follows:

1.From the main JMP taskbar, select FileNew Data Table, which results in an Untitled new data table in a separate screen. To change “Untitled” to another title, point the cursor to the “Untitled” box in the left top corner, right click twice, and enter the new title.

2. Create 2 columns, Column 1 and Column 2, in a New Data Table.

3. Enter the values 0, 1, 2, …, 12 in Column 1.

4. Label Column 2 as P(6) and right-click on P(6). Then select the Formula option. Another dialog box,P(6), appears.

5. In the dialog box P(6),select Discrete Probability option from the Functions (grouped). Scroll down the drop down menu and select the Poisson Probability (for cumulative probabilities select Poisson Distribution option).

6. In the text box below,the formula for the Poisson Probability [[Lambda] [x]] will appear. Enter the value 6 for Lambda and select Column 1 from the Table Columns,which will appear within the parentheses, for x.

7. Select Apply to have the probability values appear in Column 2, as shown below.

Example 4.12.4 (Using JMP) Two dice are thrown and the sum of the dots obtained on the uppermost faces recorded. What is the probability that a 7 occurs for the third time on the third throw? On the fourth throw? On the xth throw ()?

Solution:Consulting Example 4.9.1, we have here that and that the number of throws x needed to get sevens (event A is the event “a seven”) has probabilities given by the negative binomial distribution. To determine these probabilities using JMP, proceed as follows:

  1. From the main JMP taskbar, select FileNew Data Table, which results in an Untitled new data table in a separate screen. To change “Untitled” to another title, point the cursor to the “Untitled” box in the left top corner, right click twice, and enter the new title.

2. Create 2 columns, Column 1 and Column 2 in a New Data Table.

3. Enter the values 0, 1,… in Column 1.

4. Enter the values 3, 4,…in Column 2(the values in column 2 are the values in column 1 plus the

desired number of successes),

5. Label Column 3as NB(3,.1667) and-right click on NB(3,.1667). Then select the Formula option. Another dialog box NB(3,.1667)appears. Note here that the negative binomial probability function formula used by JMP is different from that in Equation (4.9.3). In JMP, n denotes the number of successes, k = the number of failures x – n,so that x = n + k, where x is the total number of trials needed for n successes,

6. In the dialog box NB(3,.1667), select DiscreteProbability option from the Functions (grouped). Scroll

down the menu and select the Neg Binomial Probability (for cumulative probabilities select Neg Binomial Distribution option).

7. In the text box below Neg Binomial Probability [[p] [n] [k]]will show up. Enter the

value .1667 for p, 3 for n, and select Column 1 from the Table Columns, which will appear within the parentheses, for k.

8. Select Apply to have the probability values appear in Column 3, as shown below.

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