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抛 5 枚硬币：正面 +1 反面 -1 的期望

Flip 5 coins

专题
Probability / 概率
难度
L2

题目详情

抛 5 枚公平硬币，正面得 +1、反面得 -1。问期望收益是多少？

Flip 5 coins, +1+1 per head, −1-1 per tail. What is the expected value?

解析

设正面数为 HH，则反面数 T=5−HT=5-H，收益为 H−T=2H−5H-T=2H-5。由于 E(H)=2.5E(H)=2.5，

E(收益)=2×2.5−5=0.E(\text{收益})=2\times 2.5-5=0.

Original Explanation

If HH = number of heads, T=5−HT=5-H is tails. The payout is H−T=2H−5.H - T = 2H - 5. Since E(H)=2.5,E(H)=2.5,
E(payout)=2×2.5−5=0.E(\text{payout}) = 2 \times 2.5 - 5 = 0.