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If you were to combine all the ecosystems on the planet, you would obtain the ________.

A random variable X has the following density function                     

Suppose we have 10 observations from a normal distribution with mean 10 and standard deviation 3.  Denote the sample mean and sample variance as

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

A random sample of size 100 is drawn from an exponential distribution with parameter=8.  See page 195 for the definition of the exponential distribution.   Find the value of x such that the sample mean is smaller than x with a probability of 12.3%    

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

Suppose we have 10 observations from a gamma distribution with mean 10 and variance 100.  Denote the sample mean and sample variance as 

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

A die shows up numbers one to six with probabilities 0.1, 0.1, 0.1, 0.1, 0.2, 0.4, respectively.  Roll the die four times independently. It is known that for i=1,2,3 4, the number i is not observed in the i-th roll.  What is the probability of getting the number 5 once and the number 6 once.

Assume A and B are two events with P(A)=0.41 and P(B)=0.60. Which of the following statements is always true? A.