課程名稱︰統計學一上
課程性質︰必修
課程教師︰雷立芬
開課學院：管理學院
開課系所︰國企系
考試日期（年月日）︰98.11.18
考試時限（分鐘）：三小時
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
1. The bivariate distribution of X and Y is shown as follows:
X
0 1 2
0 0.08 0.14 0.12
Y 1 0.09 0.17 0.13
2 0.05 0.18 0.04
a. Find the marginal probability distribution of X. (4%)
b. Find the marginal probability distribution of Y. (4%)
c. Compute the mean and standard deviation of X. (5%)
d. Compute the mean and standard deviation of Y. (5%)
e. Compute the coefficient of correlation between X and Y. (6%)
f. Determine the mean and standard deviation of 3X-2Y+9. (6%)
2. Three airlines serve a small town in Ohio. Airlines A has 50% of all the
scheduled flights, airlines B has 30%, and airlines C has the remaining 20%.
Their on-time rates are 80%, 65%, and 40%, respectively. A plane has just
left on time. What is the probability that is was airline B? (10%)
3. Flaws in a carpet tend to occur randomly and independently at a rate of one
every 200 square feet.What is the probability that a carpet that is 8 feet by
10 feet contains no flaws? (6%)
4. Thre are 6 red balls and 4 white balls in a box. Randomly draw 4 balls from
the box. X is assumed to be the number of red balls.
a. What's the probability of X=2 in the case of replacement during the process
of drawing?(6%)
b. Compute the mean and variance of X. (4%)
c. What's the probability of X=3 in a case of without replacement during the
process of drawing? (6%)
5. The following function is the density function for the random variable X:
f(x)=(X-1)/8, 1<x<5
a. Verify that f(x) is a density function. (5%)
b. Find the probability that X lies between 1 and 3. (4%)
c. What is the probability that X is less than 2? (4%)
6. The final marks in a statistics course are normally distributed with a mean
of 80 and a standard deviation of 12. The professor must convert all marks to
letter grades. He decides that he wants 5%. A's, 25% B's, 40% C's, 25% D's,and
5% F's. Determine the cutoff each letter grade. (10%)
7. A binomial experiment where P=0.4 is conducted. Find the probability that
in a sample of 60 the proportion of successes exceeds 0.35. (5%)
8. Independent random sample of 10 observations each are drawn from normal
populations. The parameters of these populations are
Population 1 μ=280 σ=25
Population 2 μ=270 σ=30
Find the probability that the mean of sample 1 is greater than the mean of
sample 2 by more than 25. (10%)
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 140.112.251.77