題組內容

3. (20%) A random sample \( X_{1}, X_{2}, \ldots, X_{n} \) of size \( n \) is taken from a Poisson distribution with a mean of \( \lambda \), \( 0 < \lambda < \infty \).

(b) (5%) Let \( X \) equal the number of flaws per 100 feet of a used computer tape. Assume that \( X \) has a Poisson distribution with a mean of \( \lambda \). If 40 observations of \( X \) yielded 5 zeros, 7 ones, 12 twos, 9 threes, 5 fours, 1 five and 1 six, find the maximum likelihood estimate of \( \lambda \).