112年 - 112 國立臺灣大學_碩士班招生考試試題：工程統計#119662

1. (20%) Let X be a random variable with the Poisson distribution with parameter of λ. Show that the mean and variance of X are both λ.

2. (20%) Conduct a test of goodness-of-fit to determine whether the data below follow a normal distribution with μ =65 and σ=21, using a 0.05 level of significance.

(a) Answer the question using a 0.05 level of significance.

(b) Answer the question using the P-value approach.

(c) Answer the question using a confidence interval.

4. (20%) Derive the normal equations(正規方程式)for the polynomial regression y=β_０+β₁x₁+β₂x₂+β₃x₁x₂.

(a) Determine the median of X.

(b) What percentage of the severe snow storms are over 15 inches?

(c) What is the expected amount of snowfall in the town in a severe snow storm? 23451214144

112年 - 112 國立臺灣大學_碩士班招生考試試題：工程統計#119662

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