(a) Explain without any calculations why the mean number on a die rolled should be equal to...

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(a) Explain without any calculations why the mean number on a die rolled should be equal to 3.5. Verify it proceeding from definition (2.1.1).

(b) Let us revisit Exercise 5a. Say, without calculations, in which case the mean is larger.

(c) Show that for any symmetric distribution (see a definition in Exercise 5), the expected value equals the center of symmetry.

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