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110年 - 110 國立臺灣大學_碩士班招生考試_應用數學科學研究所數理統計組:機率統計#102196
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2. (15%) Let X and Y be mutually independent and continuous random variables with the corresponding probability density functions fx(x) and fY(y). Derive the probability density function of Y conditioning on X -Y = 0.
相關申論題
1. (8%) (7%) Let 'T be a failure time with support {t1， t2,...， tn，...，) and in terms of λj's, i=l,...，...，n，...
#429965
3. (7%) (8%) Let X = Rcosθ and Y a Rsin θ, where R is a positive random variable on (0,∞), θ is a uniform random variable on (0, 2π), and R and θ are mutually independent. Derive the corresponding distributions of X/Y and 2XY/
#429967
4. (15%) Let U1,...,Un,... be independent randon variables from Uniform(0, 1) and P(X = x) = (1/(e - 1)x!) I(1,2,3,...,)(x) be the probability density function of X. Find the probability density function of Z = minf{U1,...,Ux}.
#429968
5. (7%) (8%) Let X1,..., Xn, be a random sample from Uniform(θ, θ + 1). Find a minimal suffcient statistic of θ and derive its distribution.
#429969
6. (15%) Let X1,..., Xn be a random sample from N(u，σ2), where μ andσ2 are unknown parameters. Derive the power function of the size a likelihood ratio test for the hypotheses H0 : μ ≤ μ0 versus HA : μ ＞ μ0.
#429970
7. (10%) Let X1...., Xn be a random sample from a geometric distribution P(X = x) = and p have a uniform prior distribution on (0,1). Find the Bayes estimator of p based on the loss function
#429971
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110年 - 110 國立臺灣大學_碩士班招生考試_應用數學科學研究所數理統計組:機率統計#102196
110年 · #102196
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