{"action":"created","comment":{"url":"https://api.github.com/repos/sympy/sympy-paper/pulls/comments/66581250","id":66581250,"diff_hunk":"@@ -0,0 +1,50 @@\n+%% Stats\n+The \\verb|sympy.stats| module provides random variable types and methods for\n+determination of statistical properties of expressions involving random\n+variables. The variables can be either continuous or discontinuous, which are\n+further divided into finite and infinite. They are associated\n+with probability densities on corresponding domains and internally defined\n+in terms of probability spaces. \n+Apart from the possibility of defining the random variables from user supplied\n+density distribution, SymPy provides definitions of most common\n+distributions, including \\texttt{Uniform}, \\texttt{Poisson}, \\texttt{Normal},\n+\\texttt{Binomial}, \\texttt{Bernoulli}, and many others.\n+\n+Properties of random expressions can be calculated using, e.g.,\n+\\texttt{E} and \\texttt{variance} to calculate expectation and variance.\n+Conditions on random variables can be defined with inequalities, equalities,\n+and logical operators and their overall probabilities are obtained using\n+\\texttt{P}. The features can be illustrated on a model of two dice throws:\n+\\begin{verbatim}\n+>>> from sympy.stats import Die, P, E\n+>>> X, Y = Die(\"X\"), Die(\"Y\")\n+>>> P(Eq(X, 6) & Eq(Y, 6))\n+1/36\n+>>> P(X>Y)\n+5/12\n+\\end{verbatim}\n+The conditions can also be supplied as a second parameter to \\texttt{E},\n+\\texttt{P}, and other methods to calculate the property given the condition:\n+\\begin{verbatim}\n+>>> E(X, X+Y<5)\n+5/3\n+\\end{verbatim}\n+\n+Using the facilities of the \\texttt{sympy.stats} module, one can, for\n+example, calculate \n+%Using the above-mentioned features, it is easy to calculate, for example\n+the well known properties of maxwellian velocity distribution\n+\\begin{verbatim}\n+>>> from sympy.stats import Maxwell, density\n+>>> kT, m, x = symbols(\"kT m x\", positive=True)\n+>>> v = Maxwell(\"v\", sqrt(kT/m))\n+>>> E(v)                                # mean velocity\n+2*sqrt(2)*sqrt(kT)/(sqrt(pi)*sqrt(m))\n+>>> E(m*v**2/2)                         # mean energy\n+3*kT/2\n+>>> solve(density(v)(x).diff(x), x)[0]  # most probable velocity\n+sqrt(2)*sqrt(kT)/sqrt(m)\n+\\end{verbatim}\n+\n+More information on the \\texttt{sympy.stats} module can be found in\n+\\cite{StatsMRocklin}.","path":"stats.tex","position":50,"original_position":50,"commit_id":"a1032c8fb0a6a526d4db1448c3c9194cf85c196e","original_commit_id":"a1032c8fb0a6a526d4db1448c3c9194cf85c196e","user":{"login":"Upabjojr","id":4128856,"avatar_url":"https://avatars.githubusercontent.com/u/4128856?v=3","gravatar_id":"","url":"https://api.github.com/users/Upabjojr","html_url":"https://github.com/Upabjojr","followers_url":"https://api.github.com/users/Upabjojr/followers","following_url":"https://api.github.com/users/Upabjojr/following{/other_user}","gists_url":"https://api.github.com/users/Upabjojr/gists{/gist_id}","starred_url":"https://api.github.com/users/Upabjojr/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/Upabjojr/subscriptions","organizations_url":"https://api.github.com/users/Upabjojr/orgs","repos_url":"https://api.github.com/users/Upabjojr/repos","events_url":"https://api.github.com/users/Upabjojr/events{/privacy}","received_events_url":"https://api.github.com/users/Upabjojr/received_events","type":"User","site_admin":false},"body":"@mrocklin are there other papers/links concerning _sympy.stats_ ?","created_at":"2016-06-10T08:53:54Z","updated_at":"2016-06-10T08:53:54Z","html_url":"https://github.com/sympy/sympy-paper/pull/187#discussion_r66581250","pull_request_url":"https://api.github.com/repos/sympy/sympy-paper/pulls/187","_links":{"self":{"href":"https://api.github.com/repos/sympy/sympy-paper/pulls/comments/66581250"},"html":{"href":"https://github.com/sympy/sympy-paper/pull/187#discussion_r66581250"},"pull_request":{"href":"https://api.github.com/repos/sympy/sympy-paper/pulls/187"}}},"pull_request":{"url":"https://api.github.com/repos/sympy/sympy-paper/pulls/187","id":73299207,"html_url":"https://github.com/sympy/sympy-paper/pull/187","diff_url":"https://github.com/sympy/sympy-paper/pull/187.diff","patch_url":"https://github.com/sympy/sympy-paper/pull/187.patch","issue_url":"https://api.github.com/repos/sympy/sympy-paper/issues/187","number":187,"state":"open","locked":false,"title":"Add section about sympy.stats","user":{"login":"rouckas","id":37223,"avatar_url":"https://avatars.githubusercontent.com/u/37223?v=3","gravatar_id":"","url":"https://api.github.com/users/rouckas","html_url":"https://github.com/rouckas","followers_url":"https://api.github.com/users/rouckas/followers","following_url":"https://api.github.com/users/rouckas/following{/other_user}","gists_url":"https://api.github.com/users/rouckas/gists{/gist_id}","starred_url":"https://api.github.com/users/rouckas/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/rouckas/subscriptions","organizations_url":"https://api.github.com/users/rouckas/orgs","repos_url":"https://api.github.com/users/rouckas/repos","events_url":"https://api.github.com/users/rouckas/events{/privacy}","received_events_url":"https://api.github.com/users/rouckas/received_events","type":"User","site_admin":false},"body":"It has become a bit longer than I expected and I don't even mention the sampling functionality. But I can shorten it if needed.","created_at":"2016-06-09T22:52:05Z","updated_at":"2016-06-10T08:53:54Z","closed_at":null,"merged_at":null,"merge_commit_sha":"c0bfecf36bcca2f58fce3eea33f074977ada4e7f","assignee":null,"milestone":null,"commits_url":"https://api.github.com/repos/sympy/sympy-paper/pulls/187/commits","review_comments_url":"https://api.github.com/repos/sympy/sympy-paper/pulls/187/comments","review_comment_url":"https://api.github.com/repos/sympy/sympy-paper/pulls/comments{/number}","comments_url":"https://api.github.com/repos/sympy/sympy-paper/issues/187/comments","statuses_url":"https://api.github.com/repos/sympy/sympy-paper/statuses/a1032c8fb0a6a526d4db1448c3c9194cf85c196e","head":{"label":"rouckas:stats","ref":"stats","sha":"a1032c8fb0a6a526d4db1448c3c9194cf85c196e","user":{"login":"rouckas","id":37223,"avatar_url":"https://avatars.githubusercontent.com/u/37223?v=3","gravatar_id":"","url":"https://api.github.com/users/rouckas","html_url":"https://github.com/rouckas","followers_url":"https://api.github.com/users/rouckas/followers","following_url":"https://api.github.com/users/rouckas/following{/other_user}","gists_url":"https://api.github.com/users/rouckas/gists{/gist_id}","starred_url":"https://api.github.com/users/rouckas/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/rouckas/subscriptions","organizations_url":"https://api.github.com/users/rouckas/orgs","repos_url":"https://api.github.com/users/rouckas/repos","events_url":"https://api.github.com/users/rouckas/events{/privacy}","received_events_url":"https://api.github.com/users/rouckas/received_events","type":"User","site_admin":false},"repo":{"id":60454812,"name":"sympy-paper","full_name":"rouckas/sympy-paper","owner":{"login":"rouckas","id":37223,"avatar_url":"https://avatars.githubusercontent.com/u/37223?v=3","gravatar_id":"","url":"https://api.github.com/users/rouckas","html_url":"https://github.com/rouckas","followers_url":"https://api.github.com/users/rouckas/followers","following_url":"https://api.github.com/users/rouckas/following{/other_user}","gists_url":"https://api.github.com/users/rouckas/gists{/gist_id}","starred_url":"https://api.github.com/users/rouckas/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/rouckas/subscriptions","organizations_url":"https://api.github.com/users/rouckas/orgs","repos_url":"https://api.github.com/users/rouckas/repos","events_url":"https://api.github.com/users/rouckas/events{/privacy}","received_events_url":"https://api.github.com/users/rouckas/received_events","type":"User","site_admin":false},"private":false,"html_url":"https://github.com/rouckas/sympy-paper","description":"Paper 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