Recent content by thesandbox

MME := Method of Moments Estimator

Homework Statement X1,X2,...,Xk ~iid Bin(n,p) find the MME (Method of Moments Estimator) for p Homework Equations E[X] = n⋅p Var[X] = n⋅p⋅(1-p) Var(X) = E[X2] - [E[X]]2 The Attempt at a Solution Does this look correct? n⋅p⋅(1-p) = E[X2] - n2⋅p2 E[X2] = n⋅p⋅(1-p) + n2⋅p2...

To answer my own question: it does not matter. Di6 symmetry with order 12. 6 rotation symmetries 6 reflection symmetries By Burnside's Lemma: ƒ(n) = \frac{1}{12}⋅(2⋅n + 2⋅n^{2} + 4⋅n^{3} + 3⋅n^{4} + n^{6}) Where n := # of colors ƒ(n) := # of unique colorings n = 2 ƒ(2) = 13...

Homework Statement How many ways can you color the edges of a hexagon in two colors? It is assumed two colorings are identical if there is a way to flip or rotate the hexagon. Homework Equations Orbit Stabilizer Lemma and Burnside's LemmaThe Attempt at a Solution This, implements the Orbit...

Homework Statement Create a closed form for: ƒn = 14ƒn − 1 − 32ƒn − 2 + 24ƒn − 3 Homework Equations Initial conditions: ƒ(0) = 2 ƒ(1) = 5 ƒ(2) = 11 The Attempt at a Solution Because it's 3rd order, it has me confused as how to start it. I was thinking something along the...

Yes that's right, this is a βeta distribution with a mean and variance that can be looked up. β(\alpha, \beta) β(m+1, m+1) Mean = \frac{\alpha}{\alpha + \beta} Variance = (\alpha\beta)/[(\alpha+\beta)2*(\alpha+\beta+1)]

I believe you just answered it. I'm fairly confident the pdf for the sample median is correct, however with the new limits and simplification of (x - x^2)^m should make it a little more straight forward. I'll see what happens.

Homework Statement If you were taking a random sample of size n (n=2m+1 odd) from Uni(0,1) How do you find the mean and variance of the sample median? Homework Equations In order to find the mean and variance of the sample median you need to start with the sample median itself. Using...

Figured it out. The above doesn't account for all moments (rth) MX1 + X2 = MX1(t)⋅MX2(t) MXi=e\muit + (1/2)σi2t2 Following N~(\mu1 + \mu2 , σ12 + σ22)

Homework Statement X1 ∼ N(μ1,σ12) and X2 ∼ N(μ2,σ22) Let Y = X1 + X2 Find the p.d.f. of Y & label the distribution. Homework Equations The Attempt at a Solution Not quite sure how to go about this problem. µY=E[Y]=E[X1+X2]=E[X1]+E[X2]=µ1+µ2 σY2=E[Y2] - µY2 E[X12+...