1) The probability density function of a truncated exponential random variable, T, is given by

f(t) = xe^-xt/e^-xa - e^-xb, x > 0; a<= t <= b

a) show that this is a valid density function

b) Given and independant random sample of observations from this truncated exponential distribution, t1,....., tn, say, write down the log-likelihood function for x.