[試題] 105-2 鄭明燕 機率導論 第三次小考
課程名稱︰機率導論
課程性質︰數學系必修
課程教師︰鄭明燕
開課學院：理學院
開課系所︰數學系
考試日期（年月日）︰2017/4/6
考試時限（分鐘）：30分鐘
試題 :
Quiz 3 (2017/4/6)
1. Consider a probability space (Ω,A,P).
(a) (12%) State the definition of a random variable X.
(b) (12%) If X has distribution function F, what is the distribution
function of the random variable Y = aX + b, where a,b are constants,
a ≠ 0 ?
2. (20%) People enter a gambling casino at a rate of 1 every 2 minutes. What
is the probability that at least 4 people enter the casino between 12:00
and 12:05 ?
3. Let X be a geometric random variable with parameter p.
(a) (12%) Find Var(X).
(b) (12%) Find E[1/X].
(c) (12%) Show that P{ X = n+k | X ＞ n } = P{ X = k }.
4. When coin 1 is flipped, it lands on head with probability 0.4; when coin 2
is flipped, it lands on heads with probability 0.7. One of these coins is
randomly chosen and flipped 10 times.
(a) (10%) What is the prbability that the coin lands on heads on exactly 7
of the 10 flips ?
(b) (10%) Given that the first of these ten flips lands heads, what is the
conditional probability that exactly 7 of 10 flips land on heads ?
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