Quiz 1

1.

Let , we have . Therefore the MLE .

2. (a). Let X_i = 1 if the ith apple is bad and X_i = 0 otherwise. Then

where S x_i = 3 and n = 10.

Therefore,

The posterior distribution of q is Beta with a =6 and b = 11.

(b). The Bayes estimate with respect to the squared error loss is the mean of the posterior distribution. Therefore MLE of q is