Let X1, X2, ..., Xn be a sample of n units from a population with a probability density function f (x I θ)=θxθ-1 , 00   . According to this: Examine whether {f (x I θ)=θxθ-1 , 00 } family of distributions has exponential family property.

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Q: Let X and Y has joint probability density function f(X, Y) = 81 - , 0 <x< 3, 0 <y< 3. Find E(X).

A: The joint probability density function is, fX,Y=x2y281,0&lt;x&lt;3,0&lt;y&lt;3

Q: . Let X1, X2. -X be a random sample of size n from a distrībution with probability density function…

A: Hello! As you have posted 2 different questions, we are answering the first question. In case you…

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Q: Let X and Y be continuous random variables with a joint probability density function (pdf) of the…

A: Given X and Y are continuous random variables with a joint probability density function (pdf) of the…

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A: We have given that  Then we have to find the posterior distribution of theta:

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A: Solution: you are solution given below step.

Q: 24. Let X1, X2, ..., Xn be a random sample from a population X having the probability density…

A: Given:f(x,θ)=θxθ-1;0&lt;x&lt;1,θ&gt;0.

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Q: 9. Let Y1, Y2,., Yn denote a random sample from the probability density function given by 0-1 0<y<3…

A: Solution:- Given that pdf of y f(yθ) = θ yθ-13θ , 0 ≤y≤30 , elsewhere

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Q: Let X1,..., Xn be a random sample from a population with probability density function (pdf) f(x | 0)…

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Q: Suppose X and Y have joint probability density function f(x,y)=6x,0<x<1,0<y<1-x 0,elsewhere. a.…

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Q: Find a value of k that will make f a probability density function on the indicated interval.ƒ(x) =…

A: The probability density function on the indicated interval is given by : fx=kx ; 1, 5 As we know…

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Q: Let X₁, X2, X3,..., X30 be a random sample of size 30 from a population distributed with the…

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Q: Let X be a random variable with the gamma probability density function. Derive the MSE of T=X2+2X

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Q: 2. Let X be a continuous random variable with density function f(x)= for 0≤x≤2 0, otherwise Find…

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Q: Let Y;. Yz. --.. Y, denote a random sample from the probability density function e , y20, 0,…

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Q: Let Y1,...,Yn constitute a random sample from the probability density function given by Г(20)…

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Q: Suppose that X is a continuous random variable with density function f(x). If f(x)=k for −5≤x≤3 and…

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Q: Suppose that the probability density function of X is 3x 0<x<1 elsewhere Determine the P (X<1/3), P…

A: Since you have asked multiple questions, we will solve first question for you. If you want any…

Q: Let X and Y be two continuous random variables with joint probability density function given by:…

A: We know that  COV = E( XY) - E(X)E(Y)

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A: Given : fX(x) = αxα-1    for x ∈(0,1) and  α&gt;0.

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Q: Let X₁, X2, X3,..., X30 be a random sample of size 30 from a population distributed with the…

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A: Given: The distribution of X is  fx=k×cosπx2     0≤x≤1

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Q: Show that the f(x) = 12x(1 - x)^2 is a probability density function over the interval [0, 1]. %3D

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Q: Let X1, X2,..., X, denote a random sample from the probability density function fx(x) = axa-l for r…

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Q: .Let X be a random variable with the gamma probability density function. Derive the MSE of T=X² +2X

A: Here, X~Gammaθ,n,n&gt;0,θ&gt;0 and T=X2+2X