3. Let X and Y be two continuous random variables with joint pdf 4.xy, if 0 < x < 1,0 < y < 1 f(x, y) = 0, otherwise. (a) Derive E(X) and variance of X. (b) Verify directly that E(X²Y) = E(X²)E(Y). %3D (c) Derive cov(X, Y) = E[{X – E(X)}{Y – E(Y)}], the covariance between X and Y.

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A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts.  In case…

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Q: probability

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A: Answer is 3/2

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Q: Let X and Y be two continuous random variables with joint probability density 3x function given by:…

A: We know that, Var(X)= E(X^2)-(E(X))^2 so from the given values, = (3/5)-(3/4)^2 = 3/5 -9/16 =…

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Q: 2.4 Let X1, X2, .., Xn be a random sample from a population with probability density function f(x) =…

A: The probability density function is given by, f(x) = θ(1-x)θ-1 ,0&lt;x&lt;1 In method of moment…

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Q: 2. Let X be a random variable with pdf fx(x), and Y = X². %3D (a) Find fx(x|X > 0) (b) Find fy(y|X >…

A: We have to answer questions based on conditional pdf of distribution

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Q: 5. A random sample of size 2, Yi and Y2 is drawn from the pdf fr (y; 0)323,0 < y < What must c equal…

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Q: Escalate - Show every mynute steps in DETAILED!

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Q: let X and Y have the joint density e (x+y) for 0<x,y<∞ f(x.y)= other wise then X and Y are Not…

A: Answer: Stochastically Independent.

Q: 1. Suppose that the random variables X, Y, and 2 have the joint probability density function…

A: Solution: Note: Hello! As you have posted 2 different questions, we are answering the first question…

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Types of Bias

Statistics is the study of data collection, organization, analysis, interpretation, and presentation. Statistical bias is a characteristic of a statistical technique or its findings in which the expected value deviates from the actual root quantitative parameter being estimated. According to the actual definition of bias, it refers to the tendency of a statistic to overestimate or underestimate a parameter.