神马作文网求教一道统计学数学题a fair coin is tossed twice.let X represent the nu
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求教一道统计学数学题
a fair coin is tossed twice.let X represent the number of heads obtained on the first toss and Y represent the total number of heads obtain in two tosses.
a:derive the birvariate probability distribution for the variables X and Y.
b:compute cov(X,Y)
a fair coin is tossed twice.let X represent the number of heads obtained on the first toss and Y represent the total number of heads obtain in two tosses.
a:derive the birvariate probability distribution for the variables X and Y.
b:compute cov(X,Y)
题目：一个公平的硬币被投掷了两次,用X表示第一次得到的面,Y表示第二次得到的面,
问：a：给出X,Y的概率分布
b：计算X,Y的协方差
a:因为硬币是公平的,所以每面的概率都是0.5
所以X的分布函数：F(X)=0.5,X=正面,F（X）=0.5,X等于反面.
同理Y的分布函数：F(Y)=0.5,Y=正面,F（Y）=0.5,Y等于反面.
b：因为硬币是公平的,所以投掷两次硬币是独立的,所以cov（X,Y）=0
问：a：给出X,Y的概率分布
b：计算X,Y的协方差
a:因为硬币是公平的,所以每面的概率都是0.5
所以X的分布函数：F(X)=0.5,X=正面,F（X）=0.5,X等于反面.
同理Y的分布函数：F(Y)=0.5,Y=正面,F（Y）=0.5,Y等于反面.
b：因为硬币是公平的,所以投掷两次硬币是独立的,所以cov（X,Y）=0
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