Author: Anonymous

We are given the following square dartboard with side length = 2 units, with a circle of radius 1 unit inscribed in it and a certain region shaded red (namely, the bottom half of the square + the upper semi-circle, as shown in the picture). Suppose we throw 1000 darts on the given square dartboard and 892 of them land in the red area. Use this information to estimate π.                                                         

On a particular river, overflow floods occur once every year on average. Calculate the probability of 2 overflow floods in a particular year. Assume the number of floods follows a Poisson distribution.

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)? 

Which of the following statements about the future events list (FEL) is TRUE?

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

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 .

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