A random sample 0.38,-0.49,0.03,0.21,0.12,0.14,-0.18,-0.34,0.46, -0.01 was selected from a Laplace..

A random sample 0.38,-0.49,0.03,0.21,0.12,0.14,-0.18,-0.34,0.46, -0.01 was selected from a Laplace distributionwith density f(z, b) = exp{ -212 – pi}. Use Monte Carlo simulations to estimate the p-value for testing hypothesis Ho : p = 0 against the alternative H
1
: p > 0.
Arandom sample 1.138,1.103,3.007,1.307,1.885,1.153was obtainedfrom a distribution with density
and 0 otherwise. Find the
MLE of 6, and use it to test H
o
: 6 = 1 against H
I
: 6 > 1. Find the p-value and compare it with the p-value based on 2000 Monte Carlo generations.