Consider the discrete random variable :

Who is the best teacher ever?

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

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?

TRUE OR FALSE?  Randomly select one card from a standard deck of 52 cards. Suppose we define the event A to be that the selected card is a Queen, and the event B is that the selected card is a Spade. Then A and B are independent. Note: A standard deck of playing cards contains a total of 52 cards of 4 types: 13 each of Spades, Clubs, Hearts, and Diamonds.       

Consider a family that has two children. Assume that , and that the genders of the two children are independent. What is the probability that both children are girls given that we know at least one of them is a girl? 

Write each word phrase as an algebraic expression.  Use x to represent the unknown number. 9 more than the product of -4 and a number