38. QUESTION: A small petrol station is supplied with petrol once a week. Assume that its volume X of potential sales (in units of 10, 000 litres) has the probability density function f(x) = 6(x –...

Extracted text: 38. QUESTION: A small petrol station is supplied with petrol once a week. Assume that its volume X of potential sales (in units of 10, 000 litres) has the probability density function f(x) = 6(x – 2)(3 – x) for 2 < x="">< 3="" and="" f(x)="0" otherwise.="" determine="" the="" mean="" and="" the="" variance="" of="" this="" distribution.="" what="" capacity="" must="" the="" tank="" have="" for="" the="" probability="" that="" the="" tank="" will="" be="" emptied="" in="" a="" given="" week="" to="" be="">