Let be a simple random sample of a random variable X with density function , .
Given the statistic :
Calculate a statistic ( function of ) such that its espected value is equal to .
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Let be a simple random sample of a random variable X with density function , . Given...
STATISTICS Let be a simple random sample of a given random variable with density function , , , Calculate a sufficient statistic for and an unbiased estimator for which is function of the previous sufficient statistic. Thank you for your explanations 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 imageWe were unable to transcribe this imageWe were unable...
STATISTICS Let a random simple sample of a random variable with density function , Calculate, for , a maximum likelihood estimator , and determine if it is a consistent estimator. Thank you for your explanations. We were unable to transcribe this imagef (x | θ) = e--(1-9) We were unable to transcribe this imageWe were unable to transcribe this image f (x | θ) = e--(1-9)
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
A probability density function f of a continuous random variable x satisfies all of the following conditions except a) b) c) For any a,b with , P() = d) The mean and variance of a probability density function f are both finite 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
STATISTICS. CONFIDENCE REGIONS. Let be a simple random sample of the density , . Find a confidence interval of 95% for the mean 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 imageWe were unable to transcribe this image
Let X1, X2, ..., Xn be a random sample from X which has pdf depending on a parameter and (i) (ii) where < x < . In both these two cases a) write down the log-likelihood function and find a 1-dimensional sufficient statistic for b) find the score function and the maximum likelihood estimator of c) find the observed information and evaluate the Fisher information at = 1. f(20) We were unable to transcribe this image((z(0 – 2) - )dxəz(47)...
STATISTICS. CONFIDENCE REGIONS. Let be a simple random sample of a population with density function , , Find the confidence interval of minimum amplitude based on a sufficient statistic. Thank you for your explanations. We were unable to transcribe this imagef (x | θ) = e--(1-9) We were unable to transcribe this image f (x | θ) = e--(1-9)
A Pareto distribution is often used in economics to explain a distribution of wealth. Let a random variable X have a Pareto distribution with parameter θ so that its probability distribution function is for and 0 otherwise. The parameters and are known and fixed; is a constant to be determined. a) Assuming that find the expected value and variance of ? b) Show that for 3 ≥ θ > 2 the Pareto distribution has a finite mean but infinite variance,...
Let A be a continuous random variable with probability density function Random variable D is given by ---------------------------------------------------------------------------------------------------------------- (a) What is the probability density function of D? specify the domain of D. Answer is - - (b) Find E(D) and Var(D). fa(a) = -a? 9 0<A<3 We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
Let X be a banach space such that X= C([a,b]) where - ab+ with the sup norm. Let x and f X. Show that the non linear integral equation u(x) = (sin u(y) dy + f(x) ) has a solution u X. (the integral is from a to b). 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 imageWe...