Recall the scenario of drawing names to decide who would give a Christmas present in a family of four in Exercise 11.4.10. Suppose a family of three uses the same method. 

a. Create a probability distribution for this scenario, where X is the number of people who will draw their own names. 

b. What is the expected value for the number of people who will draw their own name? 

c. What is the standard deviation for the number of people who will draw their own name? 

d. How do the expected value and standard deviation for the family of three compare to those for the family of four?

Data from Exercise 11.4.10.

One way that large families often decide who will give each other Christmas presents is to do a drawing. All the names go in a hat and each person draws a name and that is the person to whom he or she gives a gift. The problem with this method is that there is a chance that one or more people will draw their own names. The following table gives the probabilities that X people in a family of 4 will draw their own names in this process. 

Transcribed Image Text:

0 p(x) 9/24 1 8/24 2 6/24 3 0 4 1/24