Likelihood Definition and 116 Threads

L(x_1,...,x_n;p)=\Pi_{i=1}^{n}(\stackrel{n}{x_i}) p^{x_i}(1-p)^{n-x_i} Correct so far? The solution tells me to skip the \Pi: L(x_1,...,x_n;p)=(\stackrel{n}{x}) p^{x}(1-p)^{n-x} This is contradictory to all the examples in my book. Why?

L(x_1,x_2,...,x_n;\theta)=\Pi _{i=1}^n (\frac{\theta}{2})^x (1-\frac{\theta}{2})^{1-x} = (\frac{\theta}{2})^{\Sigma^n_{i=1}x_i}(1-frac{\theta}{2})^{n-\Sigma^n_{i=1}x_i} Correct so far if f(x) = (\frac{\theta}{2})^x (1-\frac{\theta}{2})^{1-x} ? lnL(x_1,x_2,...,x_n;\theta) =...

In general what do you do when some kind of data is missing from some data that follows exponential distribution. For example, say 3 observations are made by an instrument where x1=5, x2=3, but for x3 the instrument can not give a specific answer because it can't measure past 10. So the only...

Homework Statement X is exponentially distributed. 3 observations are made by an instrument that reports x1=5, x2=3, but x3 is too large for the instrument to measure and it reports only that x3 > 20 . (The largest value the instrument can measure is 10) a)What is the likelihood function...

I was under the impression that the likelihood function was simply the probability density function but viewing the parameter theta as the variable instead of the observations x. Ie p(x|theta) = L(theta|x) However, the likelihood function is no longer a probability function See Example 1...

Homework Statement pdf: f(x)=ax^(a-1) ; 0<x<1, a>0 estimate a by maximum likelihood Homework Equations let L be maximum likelihood L=(a(x[1])^(a-1))(a(x[2])^(a-1))...(a(x[n])^(a-1)) The Attempt at a Solution Im trying to make this into a nicer expression: L=a^n... (now I am...

Homework Statement Suppose X has a Poisson distribution with parameter lambda. Given a random sample of n observations, Find the MLE of lambda, and hat lambda. Find the expected value and variance of hat lambda. Show that hat lambda is a consistent estimator of lambda. Homework...

in need of help for how to do this question given probability mass function: x 1 2 3 4 p(x) 1/4(θ+2) 1/4(θ) 1/4(1-θ) 1/4(1-θ) Marbles 1=green 2=blue 3=red 4=white For 3839 randomly picked marbles green=1997 blue=32 red=906...

Let's say that two oceanic plates run into each other in a head-on collision. Pretend that one is 2000 miles from its spreading center, and the other one is 4000 miles from its spreading center. My question to you is "which one of these would subduct and why?" Bill in Miami

http://en.wikipedia.org/wiki/Maximum_likelihood What exactly does the "arg" here mean? It seems to be an unnecessary - the max L(\theta) seems to be sufficient enough. Or am I missing something? \widehat{\theta} = \underset{\theta}{\operatorname{arg\ max}}\ \mathcal{L}(\theta).

Hi, I'm taking a basic course in statistical methods, and we recently learned of maximum likelihood estimation. We defined the likelihood as a function of some parameter 'a', and found the estimator of 'a' by requiring a maximum likelihood with respect to it. As an example, we took the...

As far as I have seen on the web, this course is holy abstract. Anyone willing to discuss the difficulties in it? Are most people likely to fail it? What's the consensus?

This is the problem (t for theta): X ~ Expo(t) = t * e ^ (-t * x), x>0, t >0 0 otherwise Test H0: t <= 1 vs. H1: t >1 using the generalized likelihood ratio test where you have a random sample from X {X1, X2, ... , X50} and the sum of all Xi = 35. Use alpha =...

Can anyoe help with likelihood estimtor problems? :cry:

How do I estimate the standart deviation for the mean average of an poisson-distribution ? The mean average was estimated with the maximum-likelihood method by graphing the likelihood in dependence of the mean average, then just reading off the value for which the likelihood became maximal. Up...

http://www.space.com/searchforlife/et_betterodds_050114.html The link is good but as you can imagine, very slow. A few tries works best if needed. For some very striking government reports [NSA, CIA, USAF, etc], see also:https://www.physicsforums.com/showthread.php?t=2805