# Two different computer systems are monitored for a total of n weeks. Let Xi denote the number of breakdowns of the firs... Two different computer systems are monitored for a total of n weeks. Let Xi denote the number of breakdowns of the first system during the ith week, and suppose the Xis are independent and drawn from a Poisson distribution with parameter A1. Similarly, let Yi denote the number of breakdowns of the second system during the ith week, and assume independence with each Yi Poisson with parameter i2. Derive the mle's of 1, A2, and i -2. [Hint: Using independence, write the joint pmf (likelihood) of the Xis and Yis together.] 2T T20 T-D T T- 7-7  ##### Add Answer of: Two different computer systems are monitored for a total of n weeks. Let Xi denote the number of breakdowns of the firs...
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• ### Let Xi , X2,. … X, denote a random sample of size n > 1 from a distribution with pdf f(x:0)--x'e®, x > 0 and θ > 0. a. Find the MLE for 0 b. Is the MLE unbiased? Show your steps. c. Find... Let Xi , X2,. … X, denote a random sample of size n > 1 from a distribution with pdf f(x:0)--x'e®, x > 0 and θ > 0. a. Find the MLE for 0 b. Is the MLE unbiased? Show your steps. c. Find a complete sufficient statistic for 0. d. Find the UMVUE for θ. Make sure you indicate how you know it is the UMVUE. Let Xi , X2,. … X, denote a random sample of size n...

• ### Exercise 1. Customers at a coffee shop ask for hot, denote it X 0, or cold, denote it Xn 1, beverages according to a Bernoulli process with parameter p. Let N denote the first time that a customer wa... Exercise 1. Customers at a coffee shop ask for hot, denote it X 0, or cold, denote it Xn 1, beverages according to a Bernoulli process with parameter p. Let N denote the first time that a customer wants the same kind as their predecessor. (1) Find the PMF of N (2) What is the probability that XN+1-1? (3) Cold drinks take 30 seconds to prepare and hot drinks take 60 seconds. What is the expected time taken to serve...

• ### python coding please 1.2 Sum of the Independent Random Variables Consider a set of 'n random variables XI,Xy . . . Х,, . Let's define the random variable Y as the stinmation of all X, var... python coding please 1.2 Sum of the Independent Random Variables Consider a set of 'n random variables XI,Xy . . . Х,, . Let's define the random variable Y as the stinmation of all X, variables: A) For the case m 10 and Xis being independent uniform variables in the interval -0.5,0.5, generate 100,000 samples of Y. Use the discretization technique from the previous section for the [-5,5 interval and plot the pmf of Y B) Now increase m to...

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Two balls are placed randomly into two boxes labeled as I and II. Let X denote the number of balls in box I and Y denote the number of occupied boxes. (a) Find the joint density function of X and Y. (b) Compute E(X) and the conditional expectation E(X|Y= 1).

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• ### R and θ E (0, 1), define For x otherwise Let X, X, be i.i.d. random variables with density fo, for some unknown 0 E (0,1) 2 points possible (graded, results hidden) Let a be the number of X, which ar... R and θ E (0, 1), define For x otherwise Let X, X, be i.i.d. random variables with density fo, for some unknown 0 E (0,1) 2 points possible (graded, results hidden) Let a be the number of X, which are negative (X, < 0) and b be the number of Xi which are non-negative (X 0). (Note that the total number of samples is n a b and be careful not to mix up the roles of a and...

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