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111年 - 111 國立臺灣科技大學_碩士班招生試題：統計學(C)#120895
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2. (10%)Prove the mean and variance of the normal distribution N(μ, σ²) are μ and σ², respectively.
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1. (20%) Consider the following frequency table of observations on the random variable X. Based on these 50 observations, is a binomial (二項) distribution with a number of trials (n)=6 and a probability of success (p)=0.25 an appropriate model? Perform a goodness-of-fit test (適合度檢定) with α=0.05.
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(a)Determine the probability of exactly one accident over a 2-month period.
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(b)If fatalities (死亡) are involved in 20% of the accidents, what is the probability of fatalities occurring at this intersection over a period of 2 months? Assume that events of fatalities between accidents are statistically independent.
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4. (10%)The following data are given: Fit a polynomial (多項式) regression equation of the form
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(a)Use a 0.1 level of significance.
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(b)Use the P-value approach.
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(a)Test the hypothesis that the mean is not 17.0, using the P-value approach.
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