Interpret the Mean of a Discrete Random Variable as an Expected

question 23

Short Answer

Interpret the Mean of a Discrete Random Variable as an Expected Value
-A legendary football coach was known for his winning seasons. He consistently won nine or more games per season. Suppose $x$ equals the number of games won up to the halfway mark (six games) in a 12-game season. If this coach and his team had a probability $p = 0.8$ of winning any one game (and the winning or losing of one game was independent of another), then the probability distribution of the number $x$ of winning games in a series of six games is:
$\begin{array}{l|l}x & P(x) \\\hline 0 & 0.000064 \\1 & 0.001536 \\2 & 0.015360 \\3 & 0.081920 \\4 & 0.245760 \\5 & 0.393216 \\6 & 0.262144\end{array}$

Find the expected number of winning games in the first half of the season for this coach's football teams.

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