Expectation(mean) of a discrete random variable

Hello, good evening. I’am reading a book about statistics and got the equation the expectation or mean of a discrete random variable as:

by the book the result is 1.25
But in package Statistics or Distributions, the mean function calcs the sum(vector)/length(vector)

Are that the correct mean for calc expectations of discrete random variables?

The mean, in the most general sense, is equivalent to sum(vector)/length(vector). Trying to use mean directly to compute expectations of discrete random variables makes no sense. You have two vectors, not one, in this case, vector x and vector p_x. What you want is sum(x .* p_x).


Yep, was a bit confusing by the name mean. But I understood is sum(x * y).

Just do dot(x,px) and you get what you want.

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nice solution also

The name mean makes sense. The mean of a single vector is also the expectation of discrete random variables if each element of the vector has the same chance to picked, i.e., sum(x .* (1/length(x)) == sum(x .* p_x) when p_x = 1/length(x). So, basically, Base.mean gives you what you want for this specific case, but if the probability distribution is custom, then you need to do it yourself.

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