Distribution: Bernoulli Trials
Toss a coin n times, and record the side as variable x(face=1, back=0).
Therefore X=x1,x2,x3, xn like 1,0,0,0,1,1,….
Therefore X=x1,x2,x3, xn like 1,0,0,0,1,1,….
The mass density function if set the probability of face as p.
f(x=1, 0) = px(1-p)1-x
- Mean and variance
Expected value of x: E(x)=p
Variance of x: Var(x)=p(1-p)
Therefore Var(x)=E(x2)-[E(x)]2=p-p2=p(1-p)
- likelihood function
The likelihood function
The derivative against p:
Set the equation to 0:
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