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.

---

Definitions:

Prejudice

A preconceived opinion or judgment about someone or something that is not based on reason or actual experience; often related to negative or discriminatory beliefs.

Self-fulfilling Prophecy

A belief or expectation that directly or indirectly causes itself to become true, due to positive feedback between belief and behavior.

Ethnocentrism

Ethnocentrism is the belief in the superiority of one's own ethnic group or culture, often accompanied by a disregard or contempt for other cultures.

Ageism

Prejudice and discrimination toward older people.