Suppose that is a random variable with a mean of 6 and variance of 9, is a random variable with a mean of −10 and variance of 4, and = 2 . Find .

Let and  be two random variables such that . Assume their joint probability density function is given by:

Suppose that  and are i.i.d. random variables. How would you simulate a discrete uniform random integer between 1 and 12 (e.g., a 12-sided die toss)? 

Consider the discrete random variable :

TRUE or FALSE ? Let denote the number of tails from two fair coin tosses. Then the probability mass function for  is                                   

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Suppose that  and  have joint p.d.f.   for

 Suppose we wish to use Monte Carlo integration to approximate

In the course of a simulation study, we should stop to ask, “Does our code correctly create the simulation model we desired?” What step of the simulation study process is this? 

You are in a room with 4 friends. What is the probability that at least two of you share the same birthday?