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I am stuck at the following exercise: Let $ (X_k)_k$ be a sequence of i.i.d. Bernoulli$ (p)$ distributed RVs with $ p=1/2$ . We want to estimate $ Var(X_1) = p(1-p) = p^2 =: \tau_p^2$ by directly plugging in the natural estimator $ \widetilde{p} := \frac{1}{n}\sum_{i=1}^n X_i$ of $ p$ . We call this estimatorRead more

I am working with the following TransformedDistribution: Dist = TransformedDistribution[2 v S1 + 2 v S2 – v c, {S1 \[Distributed] BinomialDistribution[1/2 (c + t), p], S2 \[Distributed] BinomialDistribution[1/2 (c – t), 1 – p]}] This random variable has neat expressions for mean, variance, skewness, and kurtosis: (-1 + 2 p) t v -4 cRead more

From some calculation, I have a distribution of discrete data $ (i,P_i)$ and then want to get the median based on this distribution. Naive way is to create a list list = Table[Sum[p[[j]], {j, i}], {i, n}] then find the first element greater than $ 0$ : pos = Position[list, _?(# >= 0.5 &)][[1, 1]]Read more

Let $ G(t,\omega)$ be a stochastic process with a.s. continuous paths defined on a probability space $ \Omega$ with $ \omega \in \Omega$ and over a time period $ t\in[0,T]$ . $ T$ here is a constant, not a random variable. Suppose that the distribution of the process at every time point is known. IRead more

I have plotted the PDF of a particular function using $ Plot[PDF[NormalDistribution[64, 8.5333333], x], {x, 20, 100}]$ This gives the curve I want to find the probability of finding a data point in a particular region of this graph by integrating the area under the curve. I want to do this for a small sectionRead more

I am working on an install profile that needs some CKEditor plugins. For example. the template plugin. You can add the module no problem: composer require drupal/wysiwyg_templates Getting the JS plugin seems to be a bit harder. There seem to be 3 options: Using composer: { “repositories”: [ { “type”: “composer”, “url”: “https://packages.drupal.org/8” }, {Read more

I have deployed MongoDB cluster with two shards (two replica sets) with docker-compose. Unfortunately I’m having problems with chunks distribution between shards, I’m new to MongoDB and database sin general so those problems can be result of me misunderstanding the topic. The questions describing problems are at the bottom of post, below is configuration ofRead more

I am having some performance problems, and I need some advice. I understand that my code is not well written l = 86.; m = 76.; SD = 14.; function1a[x_] := CDF[NormalDistribution[l – 0.5, SD], x] – CDF[NormalDistribution[l + 0.5, SD], x]; factor1 = Sum[function1a[i], {i, 0., 200.}]; function1[x_] := If[x < 0., 0., function1a[x]*1./factor1];Read more

Let $ P$ be some unknown distribution with the following properties: $ P$ is unimodal $ P$ is bounded to some interval $ [a, b]$ $ P$ has a known variance $ Var(P)$ $ P$ has a known mean $ P$ has known differential entropy $ h(P)$ I’d like to estimate some lower bound onRead more

I’m trying to implement Zero Inflated Poisson probability distribution (ZIP) using ProbabilityDistribution. I’m using the following code: zipDistribution[l_,w_]:=ProbabilityDistribution[Switch[k,0,w+(1-w)Exp[-l],_,(1-w)l^k/k! Exp[-l]], {k, 0, \[Infinity], 1}]; however this doesn’t seem to work. For example, the probability of my random variable being equal to zero should be close to 0.1 but I get 0.000041. This is the code thatRead more