Question

Question 2 a) In a certain city, the daily consumption of water (in millions of litres) can be treated as a random variable having a Gamma distribution with ? = 3 and ? = 0.5.

i) What is the random variable? What is the expected daily consumption? [2 marks]

ii) If the daily capacity of the city is 12 million litres, what is the probability that this water supply will be inadequate on a given day?

Set up the appropriate integral but do not evaluate. [2 marks]

iii) What is the variance of the daily consumption of water?

Answer 1

i) What is the random variable?

The random variable is the daily consumption of water in millions of liters.

What is the expected daily consumption?

The expected daily consumption is the expected value of a gamma distributed variable with parameters,

  

ii) If the daily capacity of the city is 12 million litres, what is the probability that this water supply will be inadequate on a given day? Set up the appropriate integral but do not evaluate.

The probability is,

iii) What is the variance of the daily consumption of water?

The variance is,