Question 1: Assume that the five data points [0.1534, 2.007, 1.946, 3.645, 1.274] are generated from the exponential distribution with the probability density function as
$f(x) = \lambda e^{-\lambda x}$ (1)
1. Obtain the maximum likelihood estimates of $\lambda$.
2. Carry out a Wald test of the hypothesis that $\lambda = 1$.
3. Carry out a Likelihood Ratio test on the hypothesis that $\lambda = 1$.
4. Carry out a Lagrange Multiplier test on the hypothesis that $\lambda = 1$.