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.

A random variable X has a density function . Find the variance of X.

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 Y.

A prescription drug firm wants to know the effectiveness of a new drug in animal test, that is, percentage (p) of diseased animals cured after the use of the drug. So, the form has to run some tests.  The firm uses the sample proportion to estimate p and wishes that the maximum error is less than 3% with 95% confidence. Find the minimal number of tests that are required to run.