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Given a random variable $X$ which arise from a parameterized distribution $F(X;θ)$, the likelihood is defined as proportional to the probability of observed data as a function of $θ$: $\operatorname{L}(θ | x)=\operatorname{P}(X=x \mid θ)$
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Maximum likelihood of coin toss of different type?
My problem is I can't figure out the exact calculation to determine the maximum likelihood estimation of both biases. … Therefore, the likelihood function $L(p)$ is, by definition:
$$
L(p) =\prod f(x_i;p) \\
L(p)=p^{∑x_i} (1−p)^{n−∑x_i}
$$
So given the dataset $x_i$ we can maximize this equation w.r.t p. …