Consider a Random Sample $X _ { 1 } , X _ { 2 } , \ldots , X _ { n }$

Essay

Consider a random sample $X _ { 1 } , X _ { 2 } , \ldots , X _ { n }$ from the shifted exponential pdf $f ( x ; \lambda , \theta ) = \left\{ \begin{array} { l l } \lambda e ^ { - \lambda ( x - \theta ) } & x \geq \theta \\0 & \text { otherwise }\end{array} \right.$
a. Obtain the maximum likelihood estimators of $\theta \text { and } \lambda$
b. A random sample of size $n = 10$
results in the values 3.12, .65, 2.56, 2.21, 5.45, 3.43, 10.40, 8.94, 17.83, and 1.31, calculate the estimates of $\theta \text { and } \lambda$