105年 - 105 國立臺灣大學_碩士班招生考試：統計學(c)#122755

科目：研究所、轉學考(插大)◆統計學 | 年份：105年 | 選擇題數：0 | 申論題數：10

試卷資訊

選擇題 (0)

申論題 (10)

(a) What is the probability that the average time to locate 10 parts exceeds 60 seconds?

(b) What is the probability that the total time to locate 10 parts exceeds 600 seconds?

2. (10 points) f(x) = k(1+2x) for 0＜x＜2 is a probability density function. Evaluate the probability of x between 0 and 1.

3. (20 points) Show that the mean of a geometric distribution (幾何分配) with a probability of success p is 1/p.

(a) Test the hypothesis H₀: μ=11.5 versus H₁: μ≠11.5 using a=0.05.

(b) Find the P-value (approximation is sufficient).

(a) Derive the normal equations (正規方程式) for the polynomial regression ŷ=b+bx+b2x².

(b) Fit the polynomial regression equation in part (a).

6. (20 points) Severe thunderstorms have been recorded at a given station over a period of 66 years. During this period, the frequencies of severe thunderstorms observed are as follows:

Determine if the annual number of severe thunderstorms follow Poisson distribution with λ=1 thunderstorm per year, at 0.05 significance level.