Discrete and continuous probability distributions in problem solving

Probability Distributions

The variables in problem 5.1 are either discrete or continuous. Which are they and why?

Number of siblings -- continuous. This is because the number of siblings cannot change at the moment

Number of conversations -- discrete. There will be more conversations to be held between the children and the mothers.

Explain why the variable "number of dinner guests for Thanksgiving dinner" is discrete.

The variable is discrete because the number of guests can change through cancelation or extra invites.

Explain why the variable "number of miles to your grandmother's house" is continuous.

The variable is continuous because the distance cannot change and the house will not move as it is stationary.

Problem

Express P (x) =1/6; for x = 1, 2, 3, 4, 5, 6, in distribution form.

P (1) = 1/6

P (2) = 2/6 = 1/3

P (3) = 3/6 = 1/2

P (4) = 4/6 = 2/3

P (5) = 5/6

P (6) = 6/6

b. Construct a histogram of the probability distribution P (x) =1/6; for x = 1, 2, 3, 4, 5, 6, in distribution form

1/6

1/6

1/6

4/6

4/6

6/6

c. Describe the shape of the histogram in part (b)

Dog food distribution

Problem 5.18

Find the mean and standard deviation of the number of ships that arrive at a harbor on a given day

x

P (x)

xP (x)

x2

x2 P (x)

10

0.4

4

40

11

0.2

2.2

24.2

12

0.2

2.4

28.8

13

0.1

1.3

16.9

14

0.1

1.2

19.6

60

1

11.1

Mean = ? = ?[xP (x)] = 11.1

Variance = 129.5 -- (11.1)2 = 6.29

Standard Deviation = ?6.29 = 2.508

Problem 5.28

State a very practical reason why the defective item in an industrial situation might be defined to be the "success" in a binomial experiment