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Consider two discrete random variables and which take on values from the set {1,2,3,....,k}. Suppose we construct an n*n matrix P
whose elements comprise the joint PMF of the two random variables. That is, I is the element in the th row and th column of P , then Pi,j = PX,Y(i,j) = Pr(X=i, Y=j).
(a) Show that if and are independent random variables, then the matrix can be written as an outer product of two vectors. What are the components of the outer product?
(b) Show that the converse is also true. That is, show that if can be factored as an outer product, the two random variables are independent.
What is the major advantage of air carriers? How does this advantage impact the inventory levels of those firms using air transportation? Explain how this advantage relates to the choice of modes when choosing between air carriage and other modes ..
Modify the program ErgodicChain so that you can compute the basic quan- tities for the queueing example of Exercise 11.3.20. Interpret the mean recur- rence time for state 0.
What key factors of a business situation indicate the need for simulation
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Lenght Of Pregnancy. A woman wrote to Dear Abby and claimed that she gave birth 309 days after a visit from her hushand , who was in the Navy. Lengths of pegnancies have a mean of 268 days and a standard deviation of 15 days. Find the z score for 308..
Define the parameter of interest. State the hypotheses and Determine the test statistic and p-value considering any necessary assumptions Decide whether to reject or not reject the null hypothesis
Finding an X score. All Bright University will consider an applicant for its MBA program who scores 95 percent or higher on the GMAT exam. The mean and standard deviation, respectively, for this test are 578 and 94. What is the lowest score (X) th..
Show that the map phi: H->M_2(C) defined by phi(a+bi+cj+dk)=(a+b(sqrt -1),c+d(sqrt-1);-c+d(sqrt-1),a-b(sqrt-1)) is a ring homomorphism. Calculate its kernel and describe its image. Ps. Here H is the ring of integral Hamilton Quaternions and M_2(C) ..
Consider the Markov chain whose state at any time is the vector (n1, ... , nm) where ni denotes the number of balls in urn i. Guess at the limiting probabilities for this Markov chain and then verify your guess and show at the same time that the M..
Explain how the marketing analyst can use independent samples to collect the data.
What sort of conclusion did Kent Pekel come to in his discussion of integrity and ethics at the CIA? What are his recommendations?
discover card would like to test the hypothesis that the average credit score for an adult in dallas is different from
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