Question

Suppose that a survey is taken of a sample of Portuguese parents with at least one child under the age of 20 living at home. The parents are asked to report the number of days per week, X, in which they have family dinner at home. Identify which of the tables are valid probability models for X. X 0 1 2 3 4 5 6 7 P(X) -0.20 0.15 0.15 0.15 0.15 0.15 0.15 0.15 X 0 2 3 4 5 6 7 P(X) 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 X 0 2 3 4 5 6 7 P(X) 0 0.05 0.10 0.20 0.30 0.20 0.10 0.05 X 0 2 3 4 5 6 7 P(X) 0 10 10 10 10 10 25 25 X 0 1 2 3 4 5 6 7 P(X) 0.125 0.125 0.125 0.125 0.125 0.125 0.125 0.125

Answer 1

Solution:

1) Model 0ne is not valid probability model for X , because in the model probabilities are negative . Probability never be negative . Probability always lies between 0 and 1.

2) The condition for the model to be valid probability model is $\sum P(x)=1$

Model two is not valid probability model, because the sum of probabilities are 2.20 which greater than 1

$\sum P(x)\neq 1$

3) Model three is a valid probability model for X , because the sum of probabilities is 1

$\sum P(x)= 0 + 0.05 +0.10+0.20+0.30+0.20+0.10 +0.05=1$

The condition for model to be valid probability model for X is satisfied. $\sum P(x)=1$

4) Model four is not valid probability model for X, because probability lies between 0 and 1. Probability never be integer value.

5) Model five is not valid probability model for X. Because in our example sample of Portuguese parents with at least one child under the age of 20 living at home .

Therefore For X = 0 child has no probability

​​​​​

Model 3 is valid probability model for X.

Option C is correct.