Consider the function f(θ) = θ + sinθ on (0,2π). 1) Draw diagrams showing the intervals...

Consider the function f(θ) = θ + sinθ on (0,2π).

1) Draw diagrams showing the intervals where f^i and f^ii are positive or negative.

2) Find the critical points.

3) Find the local maxima and minima.

4) Find the intervals where f is concave up or down.

Expert Solution

milcah answered 2 years ago

Determine the intervals on which the function is concave up or concave down. f(θ) = 11θ + 11 sin2(θ), [0, π]

1) Find the critical numbers of the function. f(θ) = 16 cos θ + 8 sin^2 θ

1) Find the critical numbers of the function. f(θ) = 16 cos θ + 8 sin^2 θ θ=? 2) Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = x/(x^2 − x + 9), [0, 9] 3) f(x) = 3x3 + 4x2 + 7x + 5, a = 5 (f −1)'(a) = ?

Consider a Bernoulli distribution f(x|θ) = θ^x (1 − θ)^(1−x) for x = 0 and x...

Consider a Bernoulli distribution f(x|θ) = θ^x (1 − θ)^(1−x) for x = 0 and x = 1. Let the prior distribution for θ be f(θ) = 6θ(1 − θ) for θ ∈ (0, 1). (a) Find the posterior distribution for θ. (b) Find the Bayes’ estimator for θ.

Consider the function f(x) = x^3 / x − 2 1. Give the intervals of increase...

Consider the function f(x) = x^3 / x − 2 1. Give the intervals of increase and the intervals of decrease for f(x). 2. Give the location of any local maximums and local minimums on the graph of y = f(x). Give your answer(s) as a point, listing both the x-coordinates and y-coordinates. 3. List the intervals of concavity for f(x). 4. Identify any inflection points on the graph of y = f(x). Give your answer(s) as a point, listing...

1. You are given the graph of a function f. Determine the intervals where f is...

1. You are given the graph of a function f. Determine the intervals where f is increasing, constant, or decreasing. (Enter your answers using interval notation. If an answer does not exist, enter DNE.) The x y-coordinate plane is given. The curve enters the window in the second quadrant, goes down and right becoming less steep, changes direction at the point (−1, 0), goes up and right becoming more steep, passes through the approximate point (−0.58, 0.44), goes up and...

is 1. f(x/θ) = 2x/θ^2 complete sufficient statistic 2. f(x/θ) =((logθ) θ^x ) / (θ -1) complete...

is 1. f(x/θ) = 2x/θ^2 complete sufficient statistic 2. f(x/θ) =((logθ) θ^x ) / (θ -1) complete sufficient statistic?

Draw diagrams showing the components of a ball mill and movement of charge inside the mill....

Draw diagrams showing the components of a ball mill and movement of charge inside the mill. Label the important features.

Let Y1, ..., Yn be a random sample with the pdf: f(y;θ)= θ(1-y)^(θ-1) with θ>0 and...

Let Y1, ..., Yn be a random sample with the pdf: f(y;θ)= θ(1-y)^(θ-1) with θ>0 and 0<y<1. i) Obtain the minimum variance unbiased estimator ( for θ)

Let X1. . . . Xn be i.i.d f(x; θ) = θ(1 − θ)^x x =...

Let X1. . . . Xn be i.i.d f(x; θ) = θ(1 − θ)^x x = 0.. Is there a function of θ for which there exists an unbiased estimator of θ whose variance achieves the CRLB? If so, find it

Let f(x; θ) = θxθ−1 for 0 < x < 1 and θ ∈ Ω =...

Let f(x; θ) = θxθ−1 for 0 < x < 1 and θ ∈ Ω = {θ : 0 < θ < ∞}. Let X1, . . . , Xn denote a random sample of size n from this distribution. (a) Sketch the pdf of X for (i) θ = 1/2, (ii) θ = 1 and (iii) θ = 2. (b) Show that ˆθ = −n/ ln (Qn i=1 Xi) is the maximum likelihood estimator of θ. (c) Determine the...

Question