We now collect n independent copies of X denoted X$1,...,$ Xn and we apply one step of the EM algorithim$($ importante note: the E$-$step and the the M$-$step will be different from the mixture of gaussian case and need to be recomputed using the specific form of the exponential PDF$).$

The EM algorithm will always output an esimator lambda$\_$hat such that:

$1/($alpha$*$X$\_$bar$)<$ or equal to lambda$\_$hat $>$ or equal to $1/($X$\_$bar$)$

What is the smallest value of alpha?