Mathematics · Estimation Theory
Consider a distribution with probability mass function: f(x|θ) = (1-θ)/2 if x = 0; 1/2 if x = 1; θ/2 if x = 2; and 0 otherwise, where θ ∈ (0, 1). In a random sample of size 100, the observed counts of 0, 1, and 2 are 20, 30, and 50 respectively. The maximum likelihood estimate (MLE) of θ is:
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