Mathematics · Statistical Inference

Consider a discrete random variable X with the probability mass function: P(X=0) = θ/3, P(X=1) = 1 - θ/2, P(X=2) = θ/6, where θ ∈ (0,1) is an unknown parameter. In a random sample of size 90 from this distribution, the observed counts for X = 0, 1, and 2 are 20, 60, and 10, respectively. Then, the maximum likelihood estimate of θ is: