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               Which of the following is the conditional distribution of Y, given X=2? A.                        y=0                      2                            4 ———————————————————- f(y|2)          0.10                   0.10                      0.2 ——————————————————————————– B.                        y=0                      2                            4 ———————————————————- f(y|2)          0.40                   0.20                      0.40 ——————————————————————————– C.                        y=0                      2                            4 ———————————————————- f(y|2)          0.25                   0.25                      0.50 ——————————————————————————– D.    None of the above

How many distinct permutations are there of the letters in the word “SUCCESS”?

In testing a statistical hypothesis,  the p-value of the test statistic based on a random sample is 0.045.      Determine whether the following statement is correct:                  If  the significance level (or type I error) is 0.05,  we reject the null hypothesis.

A random sample of size 36 is from an exponential distribution with parameter=6.  See page 195 for the definition of the exponential distribution.   Let

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.