115年 - 115 國立臺北大學_日間學士班轉學生招生考試試題_統計學系日間學士班2、3年級 金融與合作經營學日間學士班3年級：統計學#147585

(a) \( (5\%) \) P(B|A_s)

(b) \( (5\%) \) P(B|A)

(a) \( (6\%) \) Find the joint probability mass function (pmf) of \( (X,Y) \).

(b) \( (4\%) \) Find the marginal probability mass function (pmf) and the cumulative distribution function (cdf) of X.

(c) \( (5\%) \) Compute the correlation coefficient of X and Y.

(a) \( (5\%) \) Find the cumulative density function (cdf) of Y.

(b) \( (2\%) \) Find the probability density function (pdf) of Y.

(c) \( (8\%) \) Find E(Y) and Var(Y)

(a) \( (5\%) \) What is the probability will be more than 10 minutes late?

(b) \( (5\%) \) What are the mean and variance of the flight times?

(a) \( (5\%) \) What is the point estimate of the difference between the two population means?

(b) \( (5\%) \) Find a \( 95\% \) confidence interval for the different between the two population means.

6. (10%) The following table contains observed frequencies of a sample of 500. Test for independence of the row and column variables using α=0.01 level of significance.

(a) \( (7\%) \) Complete the ANOVA table.

(b) \( (3\%) \) At the \( \alpha = 0.05 \) level of significance, test whether the average number of miles until failure for the four different brands of tires are equal.

(a) \( (5\%) \) Find the estimated regression equation for these data.

(b) \( (5\%) \) Use the estimated regression equation to predict the value of \( y \) when \( x = 7 \).

(c) \( (5\%) \) Find the coefficient of determination \( R^2 \)

(d) (5%) Use F test to test the hypotheses \( H_0 \): \( \beta_1 = 0 \) vs. \( H_a \): \( \beta_1 \neq 0 \) at 0.05 level of significance.