Two independent samples of sizes are randomly selected from two normal populations with unknow variances,   The sample means and the sample variances are as follows:  

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

Assume α=3, β=λ=2.  The lifetime (in years) for a certain type of batteries has a gamma distribution with  α and  β.  Randomly select 100 batteries. What is the expected number of batteries whose lifetimes are at most  λ years?

Two independent samples of sizes 11 and 8 are randomly selected from two normal populations with two equal but unknow variances.   Which of the following distributions should be used for developing confidence intervals and for testing hypotheses about the difference between the two population means

Consider the following data set    which are the results of a Wagner turbidity test performed on 15 samples of standard Ottawa testing sand (in microamperes).  Yuu can use the summary information: 

Randomly draw 5 cards from a deck of 52 cards without replacement.  Given that the total number of hearts, diamonds and clubs is 3, what is the probability that 1 heart is obtained?

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

The following observations are the numbers of customers in a service center in ten days.          9, 13, 8, 14, 18, 6, 11, 12, 10, 7 Find the range.

Two independent samples of sizes  are randomly selected from two normal populations with unknow variances,  Assume two variances are equal.  The sample means and the sample variances  are as follows:  

X and Y are two independent random variables.  X has a uniform distribution over interval (2,5) and Y has an exponential distribution with parameter