Which of the following statements is always true? A.  The union of two events A and B is the event consisting of all outcomes that are in both events. B.  The intersection of two events A and B is the event consisting of all outcomes that are either in A or in B. C.  The union of events A and B contains more sample points than their intersection. D.  The complement of an event A is the set of all outcomes in the sample space that are not contained in A.

The following observations are the numbers of phone calls received by a service center in ten days.                9, 13, 8, 14, 18, 5, 11, 12, 10, 7 Find the sample median.  

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               Find the covariance of X and Y:   Cov(X,Y).

A rare disease occurs with probability 0.002 in a large population.  Now we select 1000 people at random.  Find the probability that at most 3 people have contracted the disease.  

Let X and Y be two random variables such that Var(X)=2 and Var(Y)=1, and  Cov(X,Y)=

Two discrete random variables X and Y have a joint probability function f(x,y) given in the following table: f(x,y) x=0 1 2 y=0 0.30 0.12 0.18 1 0.20 0.12 0.08 Find the mean of X.

Randomly pick up 4 cards from a standard deck of 52 cards with replacement.  Find the probability that you get one heart and one diamond.   

A box contains 2000 red beans and 3000 green beans. Pick up 10 beans at random without replacement. Use X to denote the number of the red beans obtained. What is the distribution of X?

A box contains 2000 red beans and 3000 green beans. Pick up 10 beans at random without replacement. What is the probability of getting at most 2 red beans?  If applicable, you can use some approximation method to get the probability. 

Adult females have forearm lengths (in inches) that are normally distributed with mean 17.75. and variance 0.36. Find the upper quartile length of a female’s forearm – that is, a length x that is exceeded by 25% of adult females.