PMF | This is a python code for probabilistic matrix factorization in recommendation | Recommender System library

Poisson random variables are discrete: their y value is "probability" not "density". But the default behavior of histplot avoids guessing that you have discrete data, and it is choosing bins with binwidth < 1 in this case.

Because density normalization forces the area of all bars to sum to 1, that means the density value for the bar containing observations of a certain value will be greater than the probability mass on that value.

There are two relevant parameters here:

• stat="probability" will make the heights of the bars sum to 1, so they will match the PMF (assuming binwidth < 2, so that only one unique value appears in each bar)

• discrete=True, which sets binwidth=1 (and aligns the center of each bar with integral values)

  sns.histplot(data, stat='probability', discrete=True, shrink=.8)

I've also added shrink=0.8, which draws the bars a bit narrower than the binwidth; this helps emphasize the discrete nature of the data.

(Note that with discrete=True (implying binwidth=1), density and probability normalization will do the same thing so that's actually all you need, but Probability is the right y axis label to use here).

Iterate outside the array which contains the .name. That way, another array is generated for each iteration step.

In 1D case you can use cumsum to get the vectorized version of loop (assuming that both theta and p are column vectors):

You can declare it as:

I test that if you use the same data, you can get the similar minimum. In R:

Instead of .[] | … use map(…) to retain the array.

You can use a convolution of your PDFs:

I don't know what's in xG_fixtures but a good starting point would be to use a dynamic structure instead of variable names. e.g. filling a list or dataframe with your results. Also look at what changes (the goals) and what stays constant and find a way to iterate over the changing part. Be it with for loops or vectorization.

Assuming there's exactly one correct choice for each question, the random variable X which counts the number of correctly answered questions by choosing randomly is indeed binomial distributed with parameters n=45 and p=0.2. Hence, you want to calculate P(X >= 23) = P(X = 23 ) + ... + P(X = 45 ) = 1 - P(X <= 22), so there are two ways to compute it: