Let a 1. Suppose S = {2 ,3, ..., } and P(k) = , k = 2,3 ...
(a) Find the value of c that makes this a valid probability distribution. Express c in terms of a.
(b) Find P(outcome is odd). express the answer in terms of a.
Let a 1. Suppose S = {2, 3,...,} and P(k) = , k = 2, 3... Find P(outcome is less than or equal to 4). Express the answer in terms of a. We were unable to transcribe this imagea4k-1
Let a 1. Suppose S = {2, 3, ... , } and P(k) = , k = 2, 3, ... Find P(outcome is odd) . Express the answer in the terms of a. We were unable to transcribe this imagea4k-1
#4. Let , , and be a random sample from f. Find the UMVUE for We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
Doob’s Decomposition: Let be a submartingale relative to the filtration . Show that there is a martingale and a predictable sequence such that for all and . (Xm)m>o We were unable to transcribe this image(Mm)m>o (Am)m20 We were unable to transcribe this imagem>0 We were unable to transcribe this image
For , let be the order statistics of independent draws from . (1) Find the PDF of . (2) Compute . We were unable to transcribe this imageWe were unable to transcribe this image(2n+1 Unif -1,1 We were unable to transcribe this imageWe were unable to transcribe this image
STATISTICS. REGIONS OF CONFIDENCE Let be a simple random sample (n) of the density , Find the confidence interval of 95% for the variance of the population. Thank you for your explanations. We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
Let be a sample (size n = 1) from the exponential distribution, which has the pdf where is an unknown parameter. Let's define a statistic as . Is a sufficient statistic for ? We were unable to transcribe this imagef(x: λ) = Xe We were unable to transcribe this imageT(X) = 11>2 T(X) We were unable to transcribe this image
are order statistics from same distribution . Sample size is 3. Define and Finding marginal density of . We were unable to transcribe this imageplz) = 1 We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
Let be independent, identically distributed random variables with . Let and for , . (a) Show that is a martingale. (b) Explain why satisfies the conditions of the martingale convergence theorem (c) Let . Explain why (Hint: there are at least two ways to show this. One is to consider and use the law of large numbers. Another is to note that with probability one does not converge) (d) Use the optional sampling theorem to determine the probability that ever attains...
I have found answers to part a and b and just really need help with part c! and the extra if you have time. A= for part a then for part b, I have 5. Wave mechanics: (10 points) Suppose to have the following wave function (-oo 〈 x 〈 +00) r2 a for constants A and a a) Determine A, by normalize V(x). b) Use Ψ(x) to find the expectation values (a), (z2)), and σ,-V(z2,-(z c) Find the momentum...