課程名稱︰機率
課程性質︰資訊系必修(單班)
課程教師︰林守德
開課學院：電機資訊學院
開課系所︰資訊工程學系
考試日期（年月日）︰2018/4/26 14:20~17:20 pm
考試時限（分鐘）：180
試題 :
Probability2018 Midterm (Prof. Shou-de Lin)
4/26/2018 14:20-17:20pm
Total Points: 120
You can answer in either Chinese or English
1. [Short Answers 15pts]
(a) What are Prior and Posterior probabilities?
(b) What is Simpson's Paradox?
(c) What's the relationship between normal distribution and
Gamma distribution?
2. [CDF 7pts]
Below are the numbers drew independently from certain continuous
distribution. Can you plot the CDF?
[0.2 , 0.5 , 0.5 , 0.2 , 0.3 , 0.4 , 0.5 , 0.1]
3. [Axioms of Probability 9pts]
We know that probability (of an event) has to be defined given a
random experiment that is repeatable. However, we often hear sports
fans say something like "There is a 70% chance that X will win the
battle tomorrow". Since TOMORROW is non-repeatable, can you explain
what they really mean by saying the chance is 70%?
4. [Conditional Probability 7pts]
A multiple choice has 4 choices for each question. A student John has
50% chance to know the answer to the question, 25% he doesn't exactly
know the answer but can eliminate one choice, and 25% he has no idea
what could be the right choice. The teacher know that John answer one
question correctly, what's the probability he really knows the answer?
5. [Poisson 7pts]
A hotel has two phone lines for reservation. The number of calls coming
per minute into each line is i.i.d. and follows a Poisson distribution
with mean 3. What is the probability that at least two reservation
requests arrive in a minute?
6. [Expectation 7pts]
What is the probability that a random vatiable X is less than its
expected value, given X has an exponential distribution with parameter θ?
7. [Continuous RV 10pts]
Suppose that X is a continuous random variable with
2
2018t+512t
Ｍ_X(t) = e
X
(a) What is the probability density function of Y = e ?
(B) What is E[Y] ?
8. [Multivarite 12pts]
Suppose the X , X , ... , X are discrete random variable,
1 2 r
where r > 2 and have a joint probability mass fuction f :
n! x1 x2 xr
f(x, x , ...,x ) =