The following two problems extend the simulation procedure described above and can be solved along the same lines:\ (a) Show that a waiting time

x

with Exponential(2) distribution can be simulated as follows:\ Step 1: Generate

UUniform(0,1)

by using a computer.\ Step 2: Compute

-((1)/(2))*log(U)

and store the result in

x=-((1)/(2))*log(U)

.\ (b) Show that a waiting time

x

with

Exponential(\\\\theta )

distribution can be simulated as follows, where

\\\\theta >0

is any positive real number:\ Step 1: Generate

UUniform(0,1)

by using a computer.\ Step 2: Compute

-((1)/(\\\\theta ))*log(U)

and store the result in

x=-((1)/(\\\\theta ))*log(U)

. Please note: Please write up the solution in terms of

\\\\theta

, without specifying

\\\\theta

.

The following two problems extend the simulation procedure described above and can be solved along the same lines: (a) Show that a waiting time X with Exponential(2) distribution can be simulated as follows: Step 1: Generate UUniform(0,1) by using a computer. Step 2: Compute (1/2)log(U) and store the result in X=(1/2)log(U). (b) Show that a waiting time X with Exponential() distribution can be simulated as follows, where >0 is any positive real number: Step 1: Generate UUniform(0,1) by using a computer. Step 2: Compute (1/)log(U) and store the result in X=(1/)log(U). Please note: Please write up the solution in terms of , without specifying