A random variable X has the following PMF: [refer to image] a) Find E(X) b) If Y = g(X) = X^2, calculate the PMF of Y and draw the CDF of Y X = x P{X = x} -1 0.2 0 0.4 3 1 0.1 2 0.3

Q: A random variable X has the following PMF: [refer to image] a) Find E(X) b) If Y = g(X) = X^2,…

A: The PMF of X is given as:

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Q: Assume that the entire sample has 4 positive observations and 2 negatives observations.  Variable…

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A: Solution

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A: X~N(0,1)

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Q: generating function M,(t) = 2 determine the 2-t variance of X.

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A: E(S2) = (n-1/n)* sigma2  =! Sigma2  So it is biased estimator for sigma2

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A: Given that We have to show that Var(b)=σ2(X'X)-1

Q: Let B₁ and 32 denote the OLS estimators of B₁ and 2 in the regression: yi= Bo + Bixi + B2x₁2 + Ui.…

A: Let β^1 and β^2 denote the OLS estimators of β1 and β2 in the regression:yi=β0+β1xi1+β2xi2+μiLet β1^…

Q: Assume that we are conducting a Chi square test. There are 5 rows and 3 columns. Calculate degrees…

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A: Step 1: Step 2: Step 3: Step 4:

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Q: Suppose that P(A') = 0.4, P(B') = 0.5, P(An B) = 0.4. Find P(A), P(B), P(AUB), P(An B') and P(AIB).

A: given data P(A') =0.4P(B') = 0.5P(A∩B) = 0.4

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Q: Suppose W = (aX + 3Y) 2 where Y, X are two random variables with zero mean and variances 20x = 4,…

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Q: Suppose that X ~ Pareto(7). Define Y = In(X+1). If E[X] = }, then what is the variance %3D of Y?

A: The probability density function(pdf) for a random variable X~Pareto(γ) is given by fX(x)=γ(1+x)γ+1,…