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In the post by André Nicolas, in this stack, he writes that the expectation is a linear operator on events. This I can not understand, what exactly is intuitive explanation of expectation being linear? or, maybe some motivation to describe it as something linear.

Clemens Bartholdy
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    Expectation is basically an integral, and integration is linear. – Angina Seng Aug 08 '20 at 18:24
  • reading that statement gave me a heart attack. From what I know binomial distribution for finite number of trials is a discrete thing???! – Clemens Bartholdy Aug 08 '20 at 18:26
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    From one hand Mathematical expectation in discrete case is also linear and on another hand we can consider discrete case as some Stieltjes integral. – zkutch Aug 08 '20 at 18:47
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    In the discrete case you can consider expectation as a summation instead of an integral if you like, and summation is a linear operator. – saulspatz Aug 08 '20 at 18:51
  • Perhaps this helps: https://math.stackexchange.com/questions/2080030/linearity-of-expectations-why-does-it-hold-intuitively-even-when-the-r-v-s-are -- the question itself tries to give an intuition why the binomial distribution in particular has linearity of expectation, and the answers generalize to other discrete distributions. – David K Aug 08 '20 at 18:53

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