0
votes
1answer
25 views

$|p- \dfrac xn|>|q- \dfrac xn|$ $\implies$ $p^x(1-p)^{n-x}<q^x(1-q)^{n-x}$?

If $p,q \in (0,1)$ , and $ n \in \mathbb N$ be given and $x$ be given integer between $0$ and $n$ such that $|p- \dfrac xn|>|q- \dfrac xn|$ , then is it true that ...
0
votes
1answer
22 views

Literature study for Optimal Estimation Theory

It seems Optimal Estimation/Control Theory requires a lot more than undergraduate maths. Any good book that would help me get started? I have so far referred the following books but found them quite ...
0
votes
0answers
41 views

Maximization of The Likelihood Function of Vector Entries and Its Norm

I'd be happy for assistance with the maximization of the likelihood function of the following model. The Parameters Vector $ \mathbf{\Theta} = [{x}_{1}, {x}_{2}] $. The measurement vector is $ ...
2
votes
1answer
302 views

Maximum likelihood estimators, hypergeometric and binomial

I'm trying to solve a two part problem. The set up is as follows: consider a bag with $\theta$ red marbles and $7-\theta$ blue marbles, with $\theta$ being unknown. Let $x$ denote the number of red ...
1
vote
0answers
29 views

MLE estimation of parameters, converting normalized observations to integers and back

I am fitting a model's parameters to grouped data by maximizing the likelihood equation: $L(\theta)=N!\prod_{i=1}^{G}\frac{p_i(\theta)^{n_i}}{n_i!}$ $\theta$ is the vector of parameters. $n_i$ is ...