Student Name:
Consider the following probability distribution for the possible number of people living in one household (household size) then answer questions 1 to 5:
Size of
household
1
2
3
4
5
6
7
f(x)
15.80% 26.70% 33.60% 13.70%
A
5.00%
A
1) Find the value of A.
2) Find the mean of household size.
3) Find the variance of household size.
4) What is the probability of having less than 5 people living in one household?
5) Find the cumulative distribution function for household size:
Size of
1
2
3
4
5
6
7
household
f(x)
F(x)
The cafeteria at a students' dormitory, has a new menu option, they now serve fish burgers, the following distribution shows the number of students ordering fish burger at lunch and dinner:
Lunch
0
1
2
0
0.06
0.1
0.06
Dinner
1
0.1
0.2
0.1
2
0.12
0.2
0.06
6) What is the probability of having 1 student ordering a fish burger at lunch and 2 students at dinner?
7) What is the mean (expected number) of students ordering a fish burger at dinner?
8) Are the lunch and dinner demands independent of each other? (Show your proof of independence/dependence).