Suppose that X1, X2, ..., Xn is a random sample with a probability law P(x) = {0x₁ 9x, six = si x = 1, 2, 3, 4; otherwise Where is an unknown parameter. A. Get an estimator of 8 by the method of the moments. B. Prove that the estimator is unbiased.

Q: 7. Let random variable X = # of sixes on two independent rolls of a die. Fill in the chart below…

A: Part 7: The number of sixes on two independent rolls of die are 0, 1 and 2. Thus, X takes value 0, 1…

Q: (3) Suppose that 5 voters voted for candidate A and 15 for candidate B. Is it safe to conclude using…

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A:

Q: 2. If X, Y are independent random variables show that variance (X-Y)= variance (X) + variance (Y).…

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Q: 1) A random variable X is defined by: X = -2 3 1 Find the first four moments about the mean. prob.…

A: The question is about moments Given :   To find : First 4 moments about the mean

Q: Suppose that X is a random variable with mean 30 and standard deviation 4. Y is a random variable…

A: The standard deviation of X is 4 and standard deviation of Y is 8.

Q: 12 Let x1, X2, ..., Xn be a random sample from a gamma distribution with parameters a and B. If a is…

A:

Q: 7. Suppose that X is a random variable for which the m.g.f. is as follows: V(1) = -(3e' + e!) for -0…

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Q: 24. Let X1, X2, .., X 100 be a random sample of size 100 from a distribution with density S(2) = {6…

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Q: Suppose you take independent random samples from populations with means µg and µz and standard…

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Q: 5. Let the random variable X be the number of days that a certain patient needs to be in the…

A: Let x be the number of days that a patient needs to be in the hospital.Its PMF is given byConsider…

Q: Assume I observe 3 data points x1, x2, and x3 drawn independently from the same unknown probability.…

A: From given data we have : Prx1|M=0.5,Prx2|M=0.1,Prx3|M=0.2.

Q: Consider the following probability distribution where random variable X denotes the number of cups…

A: Given data is  x 0 1 2 3 4 5 P(x) 0.35 0.40 0.16   0.02 0.02

Q: 3. V, W, X and Y are independent random variables, each having a normal distribution. V has mean 4…

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Q: 5. The random variable X represents the number of cherries in a cherry puff, and has the probability…

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Q: . Let X1, X2, ., Xn be a random sample from a normal population with mean u variance o?. Xm and Så…

A: Given: X1,X2, ....... ,Xn ~Nμ, σ2Sample mean = X¯nSample variance = Sn2

Q: All random samples of size n = 9 are selected from a normal population with u = 55 and o = 10, and…

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Q: 2.5.1 The probability function of a random variable Y is given by p(i) = ,i = 0, 1, 2, positive…

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Q: 1. Let X1, X2, X3 be identically distributed independent exponential random variables and Y = X₁+ X2…

A: Given that X​1, X2​, and X3​ are identically distributed independent exponential random variables…

Q: Suppose that X is a random variable with mean 30 and standard deviation 4. Y is a random variable…

A: Given E(X)=30, sd(X)=4  E(Y)=50 , sd(Y)=8  correlation (X,Y)=0 1) Z= 35-10X 2) Z= X+Y 3) Z= -2X - 2Y…