Let c(y1, y2) = y1 + y2 + (y1y2)^ −(1/3). Does this cost function have economies...

Let c(y1, y2) = y1 + y2 + (y1y2)^ −(1/3). Does this cost function have economies of scale for y1? What about economies of scope for any strictly positive y1 and y2. Hint, economies of scope exist if for a positive set of y1 and y2, c(y1, y2) < c(y1, 0) + c(0, y2). [Hint: Be very careful to handle the case of y2 = 0 separately.]

Expert Solution

Let c(y1, y2) = y1 + y2 + (y1y2) − 1 3 Does this cost function have economies of scale for y1? What about economies of scope for any strictly positive y1 and y2. Hint, economies of scope exist if for a positive set of y1 and y2, c(y1, y2) < c(y1, 0) + c(0, y2).

Rahul Sunny answered 8 months ago

Let Y1 and Y2 have joint pdf f(y1, y2) = (6(1−y2), if 0≤y1≤y2≤1 0, otherwise. a)...

Let Y1 and Y2 have joint pdf f(y1, y2) = (6(1−y2), if 0≤y1≤y2≤1 0, otherwise. a) Are Y1 and Y2 independent? Why? b) Find Cov(Y1, Y2). c) Find V(Y1−Y2). d) Find Var(Y1|Y2=y2).

For any nonnegative integer n, let Y1 < Y2 < · · · < Y2n+1 be...

For any nonnegative integer n, let Y1 < Y2 < · · · < Y2n+1 be the ordered statistics of 2n + 1 independent observations from the uniform distribution on [−2, 2]. (i) Find the p.d.f. for Y1 and the Y2n+1. (ii) Calculate E(Yn+1). Use your intuition to justify your answer.

1. Let ρ: R2 ×R2 →R be given by ρ((x1,y1),(x2,y2)) = |x1 −x2|+|y1 −y2|. (a) Prove...

1. Let ρ: R2 ×R2 →R be given by ρ((x1,y1),(x2,y2)) = |x1 −x2|+|y1 −y2|. (a) Prove that (R2,ρ) is a metric space. (b) In (R2,ρ), sketch the open ball with center (0,0) and radius 1. 2. Let {xn} be a sequence in a metric space (X,ρ). Prove that if xn → a and xn → b for some a,b ∈ X, then a = b. 3. (Optional) Let (C[a,b],ρ) be the metric space discussed in example 10.6 on page 344...

Let Y1, Y2, . . . , Y20 be a random sample of size n =...

Let Y1, Y2, . . . , Y20 be a random sample of size n = 20 from a normal distribution with unknown mean µ and known variance σ 2 = 5. We want to test H0; µ = 7 vs. Ha : µ > 7. (a) Find the uniformly most powerful test with significance level 0.05. (b) For the test in (a), find the power at each of the following alternative values of µ: µa = 7.5, 8.0, 8.5,...

Let Y1 < Y2 < Y3 < Y4 < Y5 be the order statistics of a...

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Let Y1 < Y2 < Y3 < Y4 be the order statistics of a random sample...

Let Y1 < Y2 < Y3 < Y4 be the order statistics of a random sample of size n = 4 from a distribution with pdf f(x) = 3X2, 0 < x < 1, zero elsewhere. (a) Find the joint pdf of Y3 and Y4. (b) Find the conditional pdf of Y3, given Y4 = y4. (c) Evaluate E(Y3|y4)

Let Y1 < Y2 < Y3 < Y4 < Y5 denote the order statistics of a...

Let Y1 < Y2 < Y3 < Y4 < Y5 denote the order statistics of a random sample of size 5 from a distribution having pdf f(x) = e−x, 0 < x < ∞, zero elsewhere. show that Y4 and Y5 – Y4 are independent. Hint: First find the joint pdf of Y4 and Y5.

Let Y1, Y2, . . ., Yn be a random sample from a uniform distribution on...

Let Y1, Y2, . . ., Yn be a random sample from a uniform distribution on the interval (θ - 2, θ). a) Show that Ȳ is a biased estimator of θ. Calculate the bias. b) Calculate MSE( Ȳ). c) Find an unbiased estimator of θ. d) What is the mean square error of your unbiased estimator? e) Is your unbiased estimator a consistent estimator of θ?

Let Y = (Y1, Y2,..., Yn) and let θ > 0. Let Y|θ ∼ Pois(θ). Derive...

Let Y = (Y1, Y2,..., Yn) and let θ > 0. Let Y|θ ∼ Pois(θ). Derive the posterior density of θ given Y assuming the prior distribution of θ is Gamma(a,b) where a > 1. Then find the prior and posterior means and prior and posterior modes of θ.

5. Let Y1, Y2, ...Yn i.i.d. ∼ f(y; α) = 1/6( α^8 y^3) · e ^(−α...

5. Let Y1, Y2, ...Yn i.i.d. ∼ f(y; α) = 1/6( α^8 y^3) · e ^(−α 2y) , 0 ≤ y < ∞, 0 < α < ∞. (a) (8 points) Find an expression for the Method of Moments estimator of α, ˜α. Show all work. (b) (8 points) Find an expression for the Maximum Likelihood estimator for α, ˆα. Show all work.

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