Probability and Statistics @probnstat
𝒫robability. 𝒮tatistics. ℳachine ℒearning. 𝒟ata 𝒮cience. Joined September 2022-
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Poisson Regression Model by Claudio Czado Source: math.cit.tum.de/fileadmin/w00c…
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The MM Algorithm by Kenneth Lange Source: stat.berkeley.edu/~aldous/Colloq…
Monte Carlo Simulations and Sampling by Yen-Chi Chen
The EM Algorithm by Martin Haugh Source: columbia.edu/~mh2078/Machin…
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Let X follow a Poisson distribution such that P(X=1)=P(X=2). What is the variance of X?
Moment Generating Function in Probability
An Introduction to Stochastic Processes and Their Applications by Petar Todorovic
Ask me doubts on topics in probability/statistics. I will try my best to clear them.
Studies in Theoretical and Applied Statistics by Cira Perna and Anne Ruiz-Gazen
What is the uniformly minimum variance unbiased estimator of μ in the Normal(μ,1) model?
Lectures on Optimal Transport by Luigi Ambrosio, Elia Brué and Daniele Semola
Can you mention some applications of spectral decomposition in statistics?
Measure Theory 1 by V. I. Bogachev
What is a guaranteed eigenvalue of the transition probability matrix of a Markov chain?
How can we sample an observation from a uniform distribution on a 3-dimensional sphere?
Probability and Statistical Inference by Miltiadis C. Mavrakakis and Jeremy Penzer
Which topic in Probability or Statistics pisses you off?
Suppose X and Y are two uncorrelated random variables each taking two values. Can we say that they are independent?
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@probnstat Donwloaded, thanks!
@probnstat Wanted to ask if I may be able to contribute to your site, I have a degree In Actuarial Science and Mathematical Statistics. It would help me Study for exams while I give free content. I would not even charge?
@probnstat Is Bayesian Knowledge Tracing a HMM model?
@probnstat Aren’t rnns basically the same thing as hmms?
@probnstat It is used in mixed models calculation (that’s also why they are chill about missing data) Really cool one
@probnstat Been a long time since I've seen this question. 2?
@probnstat Let X₁,...,Xₙ be i.i.d. r.v of N(μ, 1) distr. The UMVU estimator for μ? Unbiased: An estimator is unbiased (UE) if E( \hat{\mu}) = μ. Complete: The sample mean, \overline{X} = (Σ X_i) / n, is a sufficient stat for μ. the Rao-Blackwell thm: The UMVU estimator is UE.
@probnstat Cramer-Rao, Rao-Blackwell, Lehmann-Scheffe ... but in this case, the competition is disappointingly boring, due to completeness: there's merely 1 competitor in the game for unbiased estimators.
@probnstat P(X = 1)=(e^(-λ) * λ^1) / 1! = P(X=2)=(e^(-λ) * λ^2) / 2!. Give λ = 2λ^2 / 2 thus λ = 2. For X, r. v X~P(λ) it's well known Var(X)=λ=2.
@probnstat Explain risk neutral probability in a tweet.
@probnstat How to actually fabricate a mythical biased coin
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