Suppose that X_1, ... X_n are independent Exponential random variables with density f(x: lambda ) = A exp (-lambda x) for x > 0 where lambda > 0 is an unknown parameter. Show that the r quantile of the Exponential distribution is F^-1,(T)=-lambda-1 ln(l - r). The form of the quantile function in part (a) can be used to give a quantile-quantile (QQ) pl degree t to graphically assess whether the Exponential model is reasonable for a given data set. Specifically, if x(i) Solution.

1. Suppose that X_1, ... X_n are independent Exponential random variables with density f(x:
lambda ) = A exp (-lambda x) for x > 0 where lambda > 0 is an unknown parameter. Show that
the r quantile of the Exponential distribution is F^-1,(T)=-lambda-1 ln(l - r). The form of the
quantile function in part (a) can be used to give a quantile-quantile (QQ) pl degree t to
graphically assess whether the Exponential model is reasonable for a given data set. Specifically,
if x(i)
Solution