Question

Suppose the amount of milk sold daily at a milk booth is distributed with a minimum of 200 litres and a maximum of 600 litres with probability density function f(x) = {(k, 200 ≤ x ≤ 600), (0, otherwise)

Find 

(i) the value of k

(ii) the distribution function 

(iii) the probability that daily sales will fall between 300 litres and 500 litres?

Answer 1

Given p.d.f. is f(x) = {(k, 200 ≤ x ≤ 600), (0, otherwise)

(i) Since f(x) is a p.d.f.,

(ii) Now, the probability density function f(x) = {(1/400, 200 ≤ x ≤ 600), (0, otherwise)

Integrating f(x), we get probability density function 

(iii) The probability that daily sales will fall between 300 litres and 500 litres is