[機統] 一題機率的問題
完整題目是
Electric current is transmitted from point A to point B provided at
least one of the circuits #1 through #n below is closed. If the circuits
closed independently of each other and with respective probabilities
p_i, i=1,...,n, determinethe probability that:
i) Exactly one circuit is closed;
ii) At least one circuit is closed;
iii) Exactly m circuits are closed for 0 <= m <= n;
iv) At least m circuits are closed with m as in part (iii);
v) What do parts (i)-(v) become for p_1=p_2=‧‧‧=p_n=p, say?
大概的意思是一個電流從A到B至少要有一條電路是通路(closed)
現在有n條電路 各自closed的機率是p_1到p_n
上面的意思應該對吧 我不知道有沒有誤解題目的意思
i)的答案我算是
n
Σ p_i(1-p_1)...(1-p_i-1)(1-p_i+1)...(1-p_n)
i=1
不知道對不對
ii)應該是1-(1-p_1)(1-p_2)...(1-p_n)
iii) (iv) 就不太會了 可以教我嗎？ 謝謝
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