04.1 Chances of multiple outcomes

Content and key concepts

The evaluation of the option and the correct response have already been determined.
Let's ask positives and see if they're giving one together, not one answer, but every possible outcome.
Three positive masses: 2.1.1.
Для изменения рисунка включитеJavaScript; расчёт и теория доступны далее.
The total mass must be taken into account
The following current model returns the distribution by dictionary. For the final set of mutually exclusive outcomes pi≥0 and the sum pi=1. The probability of combining several results is the sum of the respective masses. The PMF is not just an arbitrary vector: negative coordinates and sum2 are not acceptable.
Non-negatives are introduced into the lab.
Weight
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p_i=\frac{a_i}{\sum_j a_j},\qquad \sum_j a_j>0.
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Weights give p=[5,.25,.25]. The multiplication of all weights by 10 preserves the distribution. The input does not set the distribution and should stop the calculation, rather than frame a uniform answer without being noticed.
Let the numerical results of X be equal to 0.1.2 The expectation of E[X] = pixi=.75 The second moment E[x2] = 1.25, the dispersion of E [X2] to E[ X]2=6875. The expectation is not to be possible. For categories such as cat/home, it is not necessary to average ID numbers as physical values.
Boundary.
The density of the continuous random value is not PMF. The even density is [0.5] equal to 2, but integral is equal to 1. The probability of a single point at this density is 0, although the event of the point is not logically impossible. In this laboratory only discrete results.
Experiment.
Concentrate the mass in one category, then distribute it evenly. Before changing which distribution will make a greater average surprise. This is preparation for entropy, not assessing the validity of the neuronet response.
p, values = [.5,.25,.25], [0,1,2]
mean = sum(a*b for a,b in zip(p,values))
variance = sum(a*(b-mean)**2 for a,b in zip(p,values))
assert mean == .75 and variance == .6875
The code repeats the operations just taken care of.
Completely checked Python-example Chapter
Available with a separate file; the short piece shown does not replace its implementation.
Now the numbers are comparable shares. So far, no outcome has been selected.
The new certificate changes the assessment. How does this question continue?
Python examples of Chapter 04
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