Thread: Pdf

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.

Originally Posted by feage7

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

I think I know how to do this question but I am not able to because you are not using paranthesis.

Originally Posted by feage7

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

If it is a valid density its integral over the real numbers equals 1.





hence f(t) is a valid density.