9 A random variable X has a probability density function f given by f(x) = cx(5 – x) 0

Extracted text: 9 A random variable X has a probability density function f given by f(x) = cx(5 – x) 0<>< 5="0" otherwise.="" (i)="" show="" that="" c="125" (ii)="" the="" lifetime="" x="" (in="" years)="" of="" an="" electric="" light="" bulb="" has="" this="" distribution.="" given="" that="" a="" standard="" lamp="" is="" fitted="" with="" two="" such="" new="" bulbs="" and="" that="" their="" failures="" are="" independent,="" find="" the="" probability="" that="" neither="" bulb="" fails="" in="" the="" first="" year="" and="" the="" probability="" that="" exactly="" one="" bulb="" fails="" within="" two="" years.="">