A high school student flips a fair coin 20 times and obtains 10 heads. What is the probability that there is 1 head in his first two flips?      

In a small island, earthquakes occur twice per year on average. Assume the number of the earthquakes follows from a Poisson distribution. What is the probability that there are 3 to 6 earthquakes from January 1,  2029 to  December 31, 2030?

A random variable X has the following density function                     

A die shows up numbers one to six with probabilities 0.1, 0.1, 0.1, 0.1, 0.2, 0.4, respectively.  Roll the die four times independently. It is known that for i=1,2,3 4, the number i is not observed in the i-th roll.  What is the probability of getting the number 5 once and the number 6 once.

It is known that 1% of chips from a product line are defective.  A professor who bought 1000 chips found out that 30 of them are defective.   Now randomly select 200 from the 1000 chips with replacement. What is the probability that 5 are defective?

Suppose we have 10 observations from an exponential distribution with mean 10 and standard deviation 10.  Denote the sample mean and sample variance as 

Two discrete random variables X and Y have the joint probability function f(x,y): f(x,y) x=0 1 2 y=0 0.10 0.20 0.10 2 0 0.10 0.10 4 0.20 0 0.20               Determine whether X and Y are independent ,  True or False    

An engineer has 20 red marbles and 30 purple marbles. He mixes them, randomly put them in two boxes with equal numbers of marbles.  Now he randomly selects a box and takes out two marbles without replacement.  What is the probability of getting one red marble?

Roll a pair of balance dice five times. Find the probability of getting a sum of 11 once and a matching pair once.

A random sample of size 64 is from an exponential distribution with parameter =1.2.  See page 195 for the definition of the exponential distribution.    Let