機率 chebyshev's 證明題
X is r.v. with mean u and variance 0,use the chebyshev's inequality
to prove that P(X=u)=1
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最佳解答
The Chebyshev's Theorem says that any variable (regardless its distribution) will contain 100(1- 1/k2 )% of the data within u +/- k standard deviation.
Now, we have variance=0, and let k=0, we can get P( u-0 < X < u+0) = 100%, so P(X=u)=1.