On each of 200 consecutive working days ten items were rando

On each of 200 consecutive working days, ten items were randomly selected from a production line and tested for defects, with the following results: The number of defective items, say X = j, out of 10 is thought to have a binomial distribuion with parameter Specifically, this model implies that Write down the likelihood function L(theta) for these data. Find the maximum likelihood estimator for theta. Find the estimated probability, p_j for each outcome j. Compute the estimated expected frequency, np_j, for each outcome j. Calculate X^2 for these data and find the p-value for this test. Assess the fit of the model to these data.

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