Suppose $X_1,\ldots,X_n$ are a random sample of distribution with probability density function
$$ f(x) = \begin {cases} \frac{\theta}{2} & \text{}\ x=-1,1 \\ 1-\theta & \text{} \ x=0 \end {cases},0<\theta<1 $$
Determine the MLE of parameter $\theta$
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closed as too localized by Did, William, Noah Snyder, Norbert, Nate Eldredge Oct 7 '12 at 17:22
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First of all this is a discrete probability distribution and is not a density function.You need to know the observed values for $X$$_i$ for i=1,2,...,n. Then for the likelihood use terms in the product that are θ/2 when $X$$_i$=-1 or $X$$_i$=1 and 1-θ when $X$$_i$=0. You could look at this like a binomial where θ is the probability of a 1 or -1 and and 1-θ is the probability of a 0. Then the mle for θ would be the proportion of times a 1 or a -1 comes up. |
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It is the proportion of zeros in your sample. |
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