서강대학교 통계학개론 (기초통계학) 2020-2 중간 기출문제 (정답 포함)
1. 시험 정보
| 학교/과목 |
서강대학교 통계학개론 (기초통계학) |
| 시험명 |
2020-2 중간고사 |
| 문항수/형식 |
풀이형 4개 |
| 교수명 |
조성빈 교수님 |
| 정답/해설 |
✅ 있음 |
| 파일형식 |
DOCX |
2. 출제 범위 & 키워드
기초 통계 계산, 조건부확률 및 결합확률, 확률변수 분포, 정규분포 응용
📚 키워드
평균·중앙값·표준편차, 박스플롯, 베이즈 정리(P(buy|good)), 공분산·상관계수, 결합분포, 확률변수 선형변환, 정규분포 평균·분산 변화
3. 기출 미리보기
Problem 1
The data about salaries are drawn from the aged 30s. (unit: 10 million won):
{25, 41, 33, 23, 74, 31, 27, 19, 18, 26, 36}
a. Find the mean, median, range, and standard deviation.
b. Draw a box and whisker’s plot.
4. 자료 보기
[기출문제]
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Problem 1
The data about salaries are drawn from the aged 30s. (unit: 10 million won):
{25, 41, 33, 23, 74, 31, 27, 19, 18, 26, 36}
a. Find the mean, median, range, and standard deviation.
b. Draw a box and whisker’s plot.
Problem 2
A cosmetic company tries to introduce a new skin lotion in the market. Based on the pilot test, consumers have rated the product using two levels – good or poor. They also expressed their willingness to purchase – buy, and not buy. The database reveals the following information:
- About 70% of consumers are likely to buy the product.
- Among those who are likely to buy, 60% give “good” rating, 40% give “poor” rating.
- Among those who are not likely to buy, 30% give “good” rating, 70% give “poor” rating.
Predict whether a customer will be likely to buy or not, given the testing results.
P(buy|good) =
P(not buy|good) =
P(buy|poor) =
P(not buy|poor) =
Problem 3
The random variable X and Y have the following distribution.
P(X=3, Y=2) = .3
P(X=3, Y=1) = .1
P(X=2, Y=2) = .2
P(X=2, Y=1) = .4
(a) Find the mean and variance of X and Y, respectively.
(b) Find the covariance and correlation coefficient of X and Y.
(c) Build up the probability distribution of X – Y. And then compute the expected value and variance of X – Y.
(d) Compute the expected value and variance of X – Y, by using the properties of expected value and variance of random variables.
Problem 4
The cleaning division of Seoul Metropolitan Government Office takes care of trash bags across the city every morning. The contents of a trash bag are normally distributed with a mean of 20 ounces and a standard deviation of 3 ounces.
What are the mean and standard deviation of the following questions:
(a) If we decrease the size of trash bag by 3 ounces.
(b) If we combine three bags and we are interested in the average weight.
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[정답]
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Problem 1
(a) mean = 32.09, median = 27, range = 56, standard deviation (sample) = 15.55 (population sd = 14.83)
(b) five-number summary: min 18, Q1 23, median 27, Q3 36, max 74
IQR = 13, upper fence = 55.5 → 74 is an outlier, upper whisker goes to 41
Problem 2
P(buy|good) = 0.8235
P(not buy|good) = 0.1765
P(buy|poor) = 0.5714
P(not buy|poor) = 0.4286
Prediction: good → buy, poor → buy
Problem 3
(a) E[X] = 2.4, Var(X) = 0.24 / E[Y] = 1.5, Var(Y) = 0.25
(b) Cov(X,Y) = 0.10, Corr(X,Y) = 0.4082
(c) Distribution of X−Y: P(0)=0.2, P(1)=0.7, P(2)=0.1
E[X−Y] = 0.9, Var(X−Y) = 0.29
(d) E[X−Y] = E[X] − E[Y] = 0.9
Var(X−Y) = Var(X) + Var(Y) − 2Cov(X,Y) = 0.29
Problem 4
(a) mean = 17, sd = 3
(b) for the average of 3 bags: mean = 20, sd = sqrt(3) ≈ 1.732
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