10 independent rolls of a single fair 6-sided die are performed. Let π be the sum of the outcomes of all 10 rolls. Find the πΈ[π] and Var(π). (Hint: let ππ be the number on top of the die on the π π‘β roll (1 β€ π β€ 10), and observe π = π1 + π2 + β― + π10.)
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Step 1
Let \( X_i \) be the outcome of the \( i \)-th roll of the die, where \( i = 1, 2, \ldots, 10 \). The total sum of the outcomes from all 10 rolls is given by \( X = X_1 + X_2 + \ldots + X_{10} \). Show moreβ¦
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