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I need to find estimate for the unknown $\theta$ with MLE using the R language if i'm given the following sample: $2, 2, 2, 2, 2, 8, 8, 8$. The sample is obtained from a discrete distribution with the rules:

$$P(2) = \theta\quad \text{and}\quad P(8) = 1-\theta$$

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1 Answer 1

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Why R language! You could do it by hand. The estimator is $\hat{\theta}=5/8$. This a Bernoulli random variable. The MLE (of the parameter which is the probability of observing 2's) is the sample mean (proportion of 2's).

In R, it is

y <- c(1, 1, 1, 1, 1, 0, 0, 0)

thetahat <- mean(y)

print(thetahat)

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I know how to do it by hand. The assignment i have is to do it in R. –  1001 Dec 11 '12 at 12:58

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