Recent content by Aria1

Let X1, X2, …, X10 be a random sample of size ten from the Normal(3, σ^2) distribution. (a) Use the likelihood ratio test to derive a 5%-level critical region for testing H0 : σ^2 = 1 versus H1 : σ^2 ≠ 1. (b)Suppose the following ten values from the Normal(3, σ^2) distribution are observed...

So, I've gotten a little further with this one, and I think part (b) is a chi-square distribution with parameter n and part (c) is an F-distribution with parameters k-1 and n-k-1. I am still not sure just how to do part (a) though, and the concept that is actually giving me trouble is how the...

Homework Statement Let X1,X2,...,Xn be i.i.d. Normal(μ,σ2) random variables, where the sample size n≥4. For 2≤k≤n-2, we define: Xbar = (1/n)SUM(Xi) from i=1 to n Xbark = (1/k)SUMXi) from i=1 to k Xbarn-k = (1/n-k-1)SUMXi from i=k+1 to n...

Even from there, I don't really understand how to compute variance. The formula I am familiar with is Var(X) = SUM(Var(Xi)) + SUM SUM E(XiXj)-E(Xi)E(Xj), but I don't really understand how to compute these values or how to, ultimately combine all the even/odd divisions into a single variance...

That makes sense to me for the most part...I'm a little confused about where the negative went in the last step, actually. You have -(e^λ - 1)d/dλ *(1/(e^λ - 1)), but in the next step, the negative seems to disappear and I'm not sure why...am I missing something, or is that a typo? Also, I'm...

By the way, I was referring to step 4 as the first step where d/dλ appears. Thanks again for your help!

Wow, thank you, I made an integration error when finding the pmf, and you caught that. As for finding E(Y), I am a little confused about how you got from step 3 to 4 and onward...I'm not sure I've seen this method of solving a sum before. Can you explain it in a little more detail, please? It...

Homework Statement Let X and Y be two independent exponential random variables with a common rate parameter λ>0. Let W=X-Y. a)Find the pdf of W=X-Y b) Find the coefficient of kurtosis of W=X-Y Homework Equations f(x)=λe^(-λx) f(y)=λe^(-λy) f(x,y) = (λ^2)e^(-λ(x+y)) Kurtosis =...

I am having a little difficulty following your analogies...by "blue bucket" do you mean odd floor? Also, for your total expected value, you use the variable "n" which was never defined. I believe you mean "w" again, so I am going to work under that assumption. I would have said the Pr{Blue...

If not, then I am not sure how to compute an integral involving (w^k)e^(-rw)...

My solution: E(X^k) for an exponential is k!/(λ^k), so E(W^k) = k!/(3^k)+k!/(2^k)-k!/(5^k) = k!(10^k + 15^k - 6^k)/(30^k). Say λ=r, and this is exactly what you are saying, yes?

I have f(w) = 3e^(-3w)+2e^(-2w)-5e^(-5w), w>0 for the pdf, but I am not sure how to proceed to E(W^k) from here.

The (904/3) should be 248, but that does not alter the pdf

I ended up with F(w) = 0, w<-4 (1/512)((w^6)/60 - w^4 - (16/3)(w^3) + (512/5)w + (904/3)), -4≤w<0 (w+5)/10 , 0≤ w< 4 1, 4≤w From there, f(w) = (1/512)((w^5)/10 - 4w^3 - 16w^2 + (512/5)), -4<w<0...

Just to clarify where my confusion is: I integrated from (-w+λ) to (w+λ) for 0<w<λ, and from 0 to (w+λ) for λ<w. The only difference in answer is that for interval 0<w<λ, my cdf was [e^(-λ^2)][e^(λw)-e^(-λw)] and for Sally's bounds, the e^(-λ^2) at the beginning was e^(λ^2). Similarly, for...