113年 - 113 國立臺北大學_碩士班一般入學考試試題_金融與合作經營學系：統計學#147275

(a) \( (5\%) \) Red tulip, say P(R).

(b) \( (5\%) \) If the tulip is red, find the conditional probability that a bag having 15 red and 10 yellow tulips was selected.

(a) \( (10\%)\mathrm{H}0: \sigma_x^2 / \sigma_Y^2 = 1 \) against a two-side alternative with \( \alpha = 0.02 \).

(b) \( (10\%)\mathrm{H}_0: \mu_x = \mu_y \) against \( \mathrm{H}_1: \mu_x > \mu_y \) with \( \alpha = 0.01 \).

(a) \( (5\%) f(x; \theta) = \theta x^{\theta - 1}, 0 < x < 1, 0 < \theta < \infty \)

(b) \( (5\%) f(x; \theta) = 1 / \theta, 0 < x < \theta < \infty \)

4. (10%) Assume that a stock is picked from a population of stocks at random. The average return of the population of stocks is 20%, and the standard deviation of the population of stocks is 2%. To calculate the maximum of the probability that a stock picked at random from this population, which has a return less than 16% or greater than 24%.

(a) \( (7\%) \) If the poll surveys at \( 95\% \) confidence level and the sampling error is approximately \( \pm 3\% \), how large of the sample size should be interviewed at least? \( \left\{Z_{0.975} = 1.96\right\} \)

(b) \( (7\%) \) The results of the poll: Group (A,B) represents A the presidential candidate and B the vice; Group (B,A) vice versa.

(a) (8%)By the perspective of the computer system, fill up the following confusion matrix with number of cases.

(b) (4%) What are the ratios of type I error and type II error?

(c) (14%) Calculate "Accuracy ratio", "Precision ratio", "Recall ratio", "False positive ratio", "False negative ratio", "F1-score".

7. (10%)Please derive when n→∞ and small p, binomial distribution will approach to Poisson distribution.