Produce a joint probability distribution of the number of adults in the household and the number of children in the household. Answer the following questions. (150 words, 15 marks)

a. What is the probability that a randomly chosen household in the UK includes only two adults?

b. What is the probability that a randomly chosen household in the UK has three or more children?

c. What is the probability that a randomly chosen household is made up of two adults and two children?

d. Given that a household has two children, what is the probability that the household has three adults?

e. Are the number of children and the number of adults in a household independent events?

f. The state benefit system is such that households whose main earner (referent person) is either unemployed or economically inactive receives a weekly benefit determined by the number of adults and the number of children in the household according to the following formula:

=100.+50.

1. Compute the expected value of weekly benefit.

2. Compute the standard deviation of weekly benefit.

The spreadsheet is below:

https://docs.google.com/spreadsheets/d/1EZllKg7ed81isRDJMvrkhCorblqK_V-yyL9rtcfpQTM/edit?usp=sharing