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研究所、轉學考(插大)◆統計學
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105年 - 105 國立臺灣大學_碩士班招生考試：統計學(c)#122755
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3. (20 points) Show that the mean of a geometric distribution (幾何分配) with a probability of success p is 1/p.
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(d)What is the probability that he will cross within the first four gaps?
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(a) What is the probability that the average time to locate 10 parts exceeds 60 seconds?
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(b) What is the probability that the total time to locate 10 parts exceeds 600 seconds?
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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.
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(a) Test the hypothesis H0: μ=11.5 versus H₁: μ≠11.5 using a=0.05.
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(b) Find the P-value (approximation is sufficient).
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(c) Construct a two-sided confidence interval on the mean to test the hypotheses in Part (a).
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(a) Derive the normal equations (正規方程式) for the polynomial regression ŷ=b+bx+b2x².
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(b) Fit the polynomial regression equation in part (a).
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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.
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