Introductory Econometrics - Topic 1: Reviews of…
Introductory Econometrics - Topic 1: Reviews of Probability and Statistics
Thông tin đề
- Môn
- Econometrics
- Kỳ thi
- University
- Số câu
- 20 câu
- Thời gian
- 60 phút
- Đáp án
- ✓ Có giải thích
Nội dung đề (20 câu)
- Câu 1.
Which statement best distinguishes the Frequentist interpretation of probability from the Bayesian interpretation?
- A.
Frequentist probability is expressed as a decimal, while Bayesian probability is always expressed as a percentage.
- B.
Frequentist probability requires experiments that can be repeated identically many times, while Bayesian probability reflects a person's degree of belief.
- C.
The Bayesian interpretation applies only to continuous random variables.
- D.
The Frequentist interpretation was developed after the Bayesian interpretation.
- A.
- Câu 2.
A discrete random variable X takes values 0, 1, 2, 3 with probabilities 0.1, 0.2, 0.5, 0.2 respectively. Which statement about X is true?
- A.
The cumulative distribution function evaluated at x = 2 equals 0.8.
- B.
The probability mass function sums to 1.2.
- C.
The expected value of X equals 2.0.
- D.
The mode of X is 3.
- A.
- Câu 3.
If Y = 3X − 5 and Var(X) = 4, what is Var(Y)?
- A.
36
- B.
4
- C.
12
- D.
1
- A.
- Câu 4.
For a joint probability mass function p(x,y) over discrete random variables X and Y, which of the following must always hold?
- A.
p(x,y) ≤ 1 for all (x,y) and ΣΣ p(x,y) = 1.
- B.
p(x,y) must be strictly positive for every (x,y).
- C.
p(x,y) is always equal to p_X(x) × p_Y(y).
- D.
p(x,y) can exceed 1 as long as the joint sum equals 1.
- A.
- Câu 5.
Given the joint PMF with p(0,0)=0.1, p(0,1)=0.2, p(1,0)=0.3, p(1,1)=0.4, what is the marginal probability p_X(0)?
- A.
0.4
- B.
0.3
- C.
0.5
- D.
0.6
- A.
- Câu 6.
If P(X=1, Y=2) = 0.12 and P(Y=2) = 0.4, what is P(X=1 | Y=2)?
- A.
0.48
- B.
0.30
- C.
0.052
- D.
0.12
- A.
- Câu 7.
The bivariate normal distribution is fully parameterised by:
- A.
Two means and two variances only.
- B.
Two means, two variances, and one correlation coefficient.
- C.
Three means and three variances.
- D.
A single mean vector and the identity matrix.
- A.
- Câu 8.
If E(X) = 5 and E(Y) = 3, what is E(2X − 3Y + 7)?
- A.
10
- B.
8
- C.
18
- D.
22
- A.
- Câu 9.
If X and Y are independent with Var(X) = 4 and Var(Y) = 9, what is Var(2X − Y)?
- A.
5
- B.
25
- C.
−5
- D.
22
- A.
- Câu 10.
The correlation coefficient ρ(X,Y) is bounded by:
- A.
−1 ≤ ρ ≤ 0.
- B.
0 ≤ ρ ≤ 1.
- C.
−1 ≤ ρ ≤ 1.
- D.
−∞ < ρ < ∞.
- A.
- Câu 11.
The conditional expectation E(X | Y = y) is:
- A.
A constant value that does not depend on y.
- B.
A function of y.
- C.
Always equal to E(X).
- D.
Always equal to zero.
- A.
- Câu 12.
If Z₁, Z₂, Z₃ are independent standard normal random variables, then Q = Z₁² + Z₂² + Z₃² follows which distribution?
- A.
Standard normal distribution.
- B.
Chi-square distribution with 3 degrees of freedom.
- C.
t-distribution with 3 degrees of freedom.
- D.
F-distribution with (3,3) degrees of freedom.
- A.
- Câu 13.
The Student t-distribution typically arises in inference when:
- A.
The population variance σ² is known.
- B.
The population variance is unknown and must be estimated from the sample.
- C.
The sample size is greater than 1000.
- D.
The data are clearly not normally distributed.
- A.
- Câu 14.
The F-distribution F(n, m) is constructed as:
- A.
The ratio of two chi-square random variables, each divided by its own degrees of freedom.
- B.
The product of two chi-square random variables.
- C.
The difference between two chi-square random variables.
- D.
The sum of two chi-square random variables.
- A.
- Câu 15.
For the sample {2, 4, 6, 8}, the sample variance S² equals:
- A.
6.67
- B.
5
- C.
6
- D.
4
- A.
- Câu 16.
Which statement correctly describes I.I.D. random variables?
- A.
They have identical distributions but may be dependent.
- B.
They are independent but may have different distributions.
- C.
They are identically distributed and mutually independent.
- D.
They must all be continuous random variables.
- A.
- Câu 17.
An estimator is said to be unbiased if:
- A.
Its variance equals zero.
- B.
Its expected value equals the true parameter θ.
- C.
It is always equal to the sample mean.
- D.
It converges to θ as the sample size tends to infinity.
- A.
- Câu 18.
If X₁, X₂, …, Xₙ are I.I.D. with mean μ and variance σ², the variance of the sample mean is:
- A.
σ²
- B.
σ²/n
- C.
σ²/n²
- D.
n·σ²
- A.
- Câu 19.
The Central Limit Theorem (CLT) states that for I.I.D. random variables with mean μ and variance σ²:
- A.
The sample mean is exactly normally distributed for any sample size n.
- B.
For large n (typically n ≥ 30), the sample mean is approximately normally distributed regardless of the original distribution.
- C.
The original distribution must be normal for the CLT to apply.
- D.
The variance of the sample mean equals σ².
- A.
- Câu 20.
In hypothesis testing, the p-value is best described as:
- A.
The probability that the null hypothesis is true.
- B.
The smallest significance level at which the null hypothesis can be rejected given the observed data.
- C.
The probability of a Type II error.
- D.
Equal to the numerical value of the test statistic.
- A.
Đáp án và giải thích từng câu có trong chế độ .