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?

Expert Solution

orchestra answered 1 year ago

Given f(x) = 1 x 2 − 1 , f 0 (x) = −2x (x 2...

Given f(x) = 1 x 2 − 1 , f 0 (x) = −2x (x 2 − 1)2 and f 00(x) = 2(3x 2 + 1) (x 2 − 1)3 . (a) [2 marks] Find the x-intercept and the y-intercept of f, if any. (b) [3 marks] Find the horizontal and vertical asymptotes for the graph of y = f(x). (c) [4 marks] Determine the intervals where f is increasing, decreasing, and find the point(s) of relative extrema, if any....

6) Given: (a) f (x) = (2x^2)/(x^2 −1) - Calculate f ′(x) and f ″(x) -...

6) Given: (a) f (x) = (2x^2)/(x^2 −1) - Calculate f ′(x) and f ″(x) - Determine any symmetry - Find the x- and y-intercepts - Use lim f (x) x→−∞ and lim f (x) x→+∞ to determine the end behavior - Locate any vertical asymptotes - Locate any horizontal asymptotes - Find all intervals where f (x) is increasing and decreasing - Find the open intervals where f (x) is concave up or concave down

One obervation is taken from the probability model. f(x;θ)=((θ/2)^|x|)*((1-θ)^(1-|x|)) for x=-1,0,1 and θ ∈ [0,1]. We...

One obervation is taken from the probability model. f(x;θ)=((θ/2)^|x|)*((1-θ)^(1-|x|)) for x=-1,0,1 and θ ∈ [0,1]. We find that the MLE of θ is |x|. Now consider T(X) where T(X)=2 when x=1 and T(X)=0 otherwise. Show that the MLE of θ has a smaller variance than T(X).

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.

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...

Let f(x) = (x − 1)2, g(x) = e−2x, and h(x) = 1 + ln(1 − 2x). (a) Find the linearizations of f, g, and h at a =...

Let f(x) = (x − 1)2, g(x) = e−2x, and h(x) = 1 + ln(1 − 2x). (a) Find the linearizations of f, g, and h at a = 0. Lf (x) = Lg(x) = Lh(x) = (b) Graph f, g, and h and their linear approximations. For which function is the linear approximation best? For which is it worst? Explain. The linear approximation appears to be the best for the function ? f g h since it is closer to ? f g h for a larger domain than it is to - Select - f and g g and h f and h . The approximation looks worst for ? f g h since ? f g h moves away from L faster...

find the line tangent to graph of f(x) at x=0 1) f(x)=sin(x^2+x) 2)f(x)=e^2x+x+1

Find all functions f(x) with f′′(x) = 3x^3 − 2x^2 + x, f(0) = 1, and...

Find all functions f(x) with f′′(x) = 3x^3 − 2x^2 + x, f(0) = 1, and f(1) = 1.

f(x) = (2x − 3)(x 2 − 6) (a) Write formulas for f '(x) and f...

f(x) = (2x − 3)(x 2 − 6) (a) Write formulas for f '(x) and f ''(x). (b) Find all x-intercepts of f(x). (Exact answers, no decimals.) (c) Find all critical points of f(x). (x-values only; y-values not needed.) Classify them using the 1st or 2nd derivative test. (d) Find all inflection points of f(x). (x-values only; y-values not needed.)

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