Statistics 简明教程
Statistics - Multinomial Distribution
多项式实验是一种统计实验,由 n 个重复试验组成。每个试验都有离散数量的可能结果。在任何给定的试验中,特定结果发生的概率都是恒定的。
A multinomial experiment is a statistical experiment and it consists of n repeated trials. Each trial has a discrete number of possible outcomes. On any given trial, the probability that a particular outcome will occur is constant.
Formula
其中——
Where −
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${n}$ = number of events
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${n_1}$ = number of outcomes, event 1
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${n_2}$ = number of outcomes, event 2
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${n_x}$ = number of outcomes, event x
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${P_1}$ = probability that event 1 happens
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${P_2}$ = probability that event 2 happens
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${P_x}$ = probability that event x happens
Example
Problem Statement:
Problem Statement:
三个纸牌玩家进行一系列比赛。玩家 A 赢得任何一局游戏的概率为 20%,玩家 B 获胜的概率为 30%,而玩家 C 获胜的概率为 50%。如果他们玩 6 场比赛,玩家 A 赢得 1 场比赛、玩家 B 赢得 2 场比赛,而玩家 C 赢得 3 场比赛的概率是多少?
Three card players play a series of matches. The probability that player A will win any game is 20%, the probability that player B will win is 30%, and the probability player C will win is 50%. If they play 6 games, what is the probability that player A will win 1 game, player B will win 2 games, and player C will win 3?
Solution:
Solution:
给出:
Given:
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${n}$ = 12 (6 games total)
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${n_1}$ = 1 (Player A wins)
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${n_2}$ = 2 (Player B wins)
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${n_3}$ = 3 (Player C wins)
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${P_1}$ = 0.20 (probability that Player A wins)
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${P_1}$ = 0.30 (probability that Player B wins)
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${P_1}$ = 0.50 (probability that Player C wins)
将这些值代入公式,即可得到:
Putting the values into the formula, we get: