SJLI. Suppose **the **binomial pdf described in Example 5.8.2 refers to the number of votes a candidate migh t receive in a poll conducted before the general election. Moreover, suppose a beta prior distribution has been assigned to *e, *and every indicator suggests the election will be close. The pollster, then, has good reason **for **concentrating the bulk

of the prior distribution around the val ue *8 *= }. Setting the two beta parameters *r*

and s both equal to 135 will accomplish that objective (in the event *r *= *s *= 135, the probability of *e *being between 0.45 and *0.55 *is approximately 0.90).

(a) Find the corresponding posterior distribution.

(b) Fi nd the squared-error Joss Bayes estimate for *() *and express it as a weighted

average of the maximum likelihood estimate *for e *and the mean of the prior pdf.

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