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 

The following observations are the numbers of customers in a service center in ten days.                9, 9, 8, 13, 19, 5, 11, 12, 10, 8 Find the 10% trimmed mean.

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:  

In a state, wildfires occur 4 times every year on average. Assume the number of wildfires follows from Poisson distribution.  Find the probability that from 13 to 15 wildfires can occur from January 1, 2029 to December 31, 2032?  

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