課程名稱︰高等生物統計法(二)
課程性質︰系選修
課程教師︰蘇秀媛
開課學院：生農院
開課系所︰農藝系
考試日期（年月日）︰99.11.19
考試時限（分鐘）：120分鐘
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
請寫出詳細的演算過程
1. For each the following p.d.f., determine the constant C, and then depict
each p.m.f. as a bar graph:
(a) f(x) = c(1/4)^x, x = 1,2,3,...
(b) f(x) = c(x+1)^2, x = 0,1,2,3
(c) f(x) = x/c, x = 1,2,3,...,n
(d) f(x) = c/[(x+1)(x+2)], x = 0,1,2,3,...
2. Find the distribution of r.v. X for each of the following m.g.f.
(a) M(t) = e^t/(2-e^t), t < ln2
(b) M(t) = e^[2(e^t-1)]
(c) M(t) = [(1/3)e^t + 2/3]^5
10
(d) M(t) = Σ(0.1)e^(tx)
x=1
3. Let X equal the number of green peanut M&Ms' in packages of size 22. 45
observations of X are:
outcome (x) : 0 1 2 3 4 5 6 7 8 9
frequency : 0 2 4 5 7 9 8 5 3 2
(a) calculate sample mean and sample variance,
(b) draw a relative frequency histogram with an appropriate Poisson
probability histogram superimposed.
4. Find the mean and the variance (from p.d.f.),
(a) Negative binomial distribution
(b) hypergeometric distribution
5. Find m.g.f. for
(a) Negative binomial distribution
(b) Binomial distribution
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