If we express x = re^jθ, enter θ such that -pi < θ < pi.
Express x and y in terms of trigonometric ratios of θ. (Express your answer in terms of θ only.)
Show that the sum of the observations of a random sample of size n from gamma distribution with parameters 1 and θ (so f(x:0)-e-re, x > 0 ) is sufficient for θ, using x/θ the definition ofsuficiency. Then show that the mle of θ is a function of the sufficient statistic.
Show that the sum of the observations of a random sample of size n from gamma distribution with parameters 1 and θ (so f(x:0)-e-re, x > 0 ) is...
Solve this equation for 1≤θ≤pi: √2 cos θ+ √2=0 a. pi/4 b. 2pi/3 c. pi d. 3pi/4
Fx(x; θ)=1/ θ for 0<x< θ. We want to test H0: θ=1 and H1 : θ>1. To do this, we take a single observation X1 of X and we reject H0 if X1> 0.9 . 1. what is the probabilty of Type I error? (false positive, probability = α) 2. what is the value of ß ( type 2 erros ) if θ=1.5? error type ressources: https://en.wikipedia.org/wiki/Type_I_and_type_II_errors
Let X1, . . . , Xn ∼ Geo(θ), f(x)= θ(1-θ)^x, and we wish to test H0 : θ ≤ 1/3 vs H1 : θ > 1/3. a) Using the full sample, X1....Xn, find the form of the UMP test for the hypotheses H0: θ=1/3 vs H1: θ=1/2. b)If n=15 and α = 0.1, what is the rejection region and the size of test in (a)?
Let X1, . . . , Xn ∼ Geo(θ), f(x)= θ(1-θ)^x, and we wish to test H0 : θ ≤ 1/3 vs H1 : θ > 1/3. a) Using the full sample, X1....Xn, find the form of the UMP test for the hypotheses H0: θ=1/3 vs H1: θ=1/2. b)If n=15 and α = 0.1, what is the rejection region and the size of test in (a)?
1. Express the point given in Cartesian coordinates in
cylindrical coordinates (r,θ,z). (9(√3/2), 9(1/2), 1)=
2. Express the point given in Cartesian coordinates in spherical
coordinates (ρ,θ,ϕ). (7/3√3,21/4,7/2) =
I know we are only supposed to post 1 per question however for
this one I have 1 part correct, I just need some help with the
rest. Please if you have the time help with question 2. Thank you
for your time and knowledge.
(1 point) Express the point given...
X, be a random sample from a distribution with the probability density function f(x; θ) = (1/02).re-z/. 0 <エく00, 0 < θ < oo. Find the MLE θ
We can sometimes re-express non-normal variables with a mathematical transformation to make them more normal.
3x2 for 0 < x < θ and zero otherwise. With the parameter θ > 0. We wish to Consider the pdf,f(x) estimate θ using the sample maximum from a random sample (iid) of size n. 0n-maxi Xi. (hint: first find the CDF and PDF of the estimator) Show this estimator is consistent a. b. Show this estimator is biased C. Suggest a better estimator and show that it is UC d. Show that n(9-an) converges (using the original estimator,...