UCLA ECON 41 - STATISTICS FOR ECONOMISTS
MIDTERM EXAM VERSION A | QUESTIONS AND
COMPLETE SOLUTIONS | SUMMER SESSION C 2026
150 Questions with Answers and Detailed Rationales
100 PERCENT GUARANTEED PASS
INSTANT DOWNLOAD ANSWERS INCLUDED
IMPORTANCE OF THIS DOCUMENT
This comprehensive examination preparation guide has been meticulously developed to help you succeed in the
UCLA ECON 41 - STATISTICS FOR ECONOMISTS MIDTERM EXAM VERSION A | QUESTIONS AND
COMPLETE SOLUTIONS | SUMMER SESSION C 2026. It contains 150 carefully selected questions that reflect
the most current exam content and testing strategies. Each question is accompanied by a correct answer and a
detailed rationale that explains the underlying pathophysiology, pharmacology, or clinical reasoning.
Self-Assessment – Test your knowledge and Exam Preparation – Familiarize yourself with the
identify areas requiring further question format and content
study areas
Concept Reinforcement – Deepen your Confidence Building – Develop test-taking
understanding through strategies and reduce
evidence-based exam anxiety
rationales
Time Management – Practice answering
questions under simulated
exam conditions
Review Summary 150 Questions
Foundations - Application - UCLA ECON 41 Statistics FOR Economists Version A AND Complete Solutions
Summer Session C 2026 Statistics FOR Economists Undergraduate YEAR 2-3 Lower Division Quantitative
Economics
All answers with rationales
,Table of Contents
Content Area Questions Key Topics
Descriptive Statistics AND 1-25 Sample, Standard, Random, Population, Deviation
DATA Display
Probability Theory AND 26-50 Sample, Regression, Standard, Confidence Interval, Slope
Rules
Discrete Random Variables 51-75 Sample, Standard, Population, Distribution, Independent
AND Probability Distributions
Continuous Random 76-100 Sample, Regression, Yields, Interval, Class
Variables AND THE Normal
Distribution
Sampling Distributions AND 101-125 Standard, Sample, Population, Confidence Interval, Error
THE Central Limit Theorem
Point Estimation AND 126-150 Sample, Regression, Standard, Error, Researcher
Confidence Intervals
TOTAL 150 All questions include answers and detailed rationales
,Section A - Descriptive Statistics AND DATA Display
Q1.
A sample of 8 hourly wages (in dollars) has a mean of 22 and a median of 25. If the largest
observation increases by 10 while all others stay the same, which statement is correct?
A. Both the mean and median increase by B. The mean increases, but the median
10. stays at 25.
C. The median increases, but the mean D. Neither the mean nor the median
stays at 22. changes.
Correct: B - The mean increases, but the median stays at 25.
Rationale:The mean is sensitive to every observation, so raising the largest value by 10
raises the mean by 10/8 = 1.25. The median depends only on the middle order statistics,
which are unaffected when the largest value increases. Thus the mean rises while the median
remains 25.
Why the other answers are wrong:
A. The median is a positional measure and does not respond to changes in the extreme value.
C. The mean is not robust to outliers, so it must change when an observation changes.
D. The mean necessarily responds to any change in an observation's value.
Reference: Stock & Watson, Introduction to Econometrics, 4th Ed., Ch. 3 (Measures of Location)
Q2.
In a survey of UCLA economics majors, 60% have taken calculus, 50% have taken
statistics, and 30% have taken both. Given a randomly selected student has taken
statistics, what is the probability they have also taken calculus?
A. 0.30 B. 0.50
C. 0.60 D. 0.80
Correct: C - 0.60
Rationale:By definition of conditional probability, P(Calculus | Statistics) = P(both) /
P(Statistics) = 0..50 = 0.60. The joint probability is divided by the conditioning event's
marginal probability.
Why the other answers are wrong:
A. 0.30 is the joint probability P(both), not the conditional probability requested.
B. 0.50 is P(Statistics) alone and ignores the conditioning information.
D. 0.80 would result from an incorrect operation such as 0.30 + 0.50.
Reference: Ross, A First Course in Probability, 10th Ed., Ch. 3 (Conditional Probability)
Page 3
, Section A - Descriptive Statistics AND DATA Display
Q3.
A random variable X has E[X] = 4 and Var(X) = 9. Define Y = 2X 5. What are E[Y] and
Var(Y)?
A. E[Y] = 3, Var(Y) = 13 B. E[Y] = 3, Var(Y) = 36
C. E[Y] = 8, Var(Y) = 18 D. E[Y] = 3, Var(Y) = 18
Correct: B - E[Y] = 3, Var(Y) = 36
Rationale:By linearity, E[Y] = 2E[X] " 5 = 2(4) " 5 = 3. Variance scales by the square of the
multiplicative constant: Var(Y) = 2² Var(X) = 4(9) = 36; additive constants do not affect
variance.
Why the other answers are wrong:
A. 13 incorrectly adds the constant 5 to the variance instead of recognizing Var is invariant to
shifts.
C. 8 mistakenly uses E[X] = 4 without applying the transformation to the mean.
D. 18 incorrectly scales variance by 2 rather than 2².
Reference: Wackerly et al., Mathematical Statistics with Applications, 7th Ed., Ch. 3 (Expected Value)
Q4.
The number of defective microchips in a batch of 20 follows a binomial distribution with n
= 20 and p = 0.05. Which expression gives P(X = 2)?
A. C(20,2)(0.05)²(0.95)¹ B. C(20,2)(0.05)¹(0.95)²
C. (0.05)²(0.95)¹ D. C(20,2)(0.05)²(0.95)²
Correct: A - C(20,2)(0.05)²(0.95)¹
Rationale:The binomial pmf is P(X = k) = C(n,k) p^k (1"p)^(n"k). With n = 20, k = 2, p = 0.05,
this yields C(20,2)(0.05)²(0.95)¹, where the binomial coefficient counts the ways to choose
which 2 chips are defective.
Why the other answers are wrong:
B. The exponents on p and (1p) are swapped; p must be raised to the number of successes k =
2.
C. Omits the binomial coefficient C(20,2) that counts the arrangements of the two successes.
D. Uses exponent 20 on (0.95) instead of n k = 18.
Reference: Newbold et al., Statistics for Business and Economics, 9th Ed., Ch. 4 (Binomial Distribution)
Q5.
A continuous random variable X has density f(x) = kx on the interval [0, 2] and 0
elsewhere. What is the value of k?
Page 4
MIDTERM EXAM VERSION A | QUESTIONS AND
COMPLETE SOLUTIONS | SUMMER SESSION C 2026
150 Questions with Answers and Detailed Rationales
100 PERCENT GUARANTEED PASS
INSTANT DOWNLOAD ANSWERS INCLUDED
IMPORTANCE OF THIS DOCUMENT
This comprehensive examination preparation guide has been meticulously developed to help you succeed in the
UCLA ECON 41 - STATISTICS FOR ECONOMISTS MIDTERM EXAM VERSION A | QUESTIONS AND
COMPLETE SOLUTIONS | SUMMER SESSION C 2026. It contains 150 carefully selected questions that reflect
the most current exam content and testing strategies. Each question is accompanied by a correct answer and a
detailed rationale that explains the underlying pathophysiology, pharmacology, or clinical reasoning.
Self-Assessment – Test your knowledge and Exam Preparation – Familiarize yourself with the
identify areas requiring further question format and content
study areas
Concept Reinforcement – Deepen your Confidence Building – Develop test-taking
understanding through strategies and reduce
evidence-based exam anxiety
rationales
Time Management – Practice answering
questions under simulated
exam conditions
Review Summary 150 Questions
Foundations - Application - UCLA ECON 41 Statistics FOR Economists Version A AND Complete Solutions
Summer Session C 2026 Statistics FOR Economists Undergraduate YEAR 2-3 Lower Division Quantitative
Economics
All answers with rationales
,Table of Contents
Content Area Questions Key Topics
Descriptive Statistics AND 1-25 Sample, Standard, Random, Population, Deviation
DATA Display
Probability Theory AND 26-50 Sample, Regression, Standard, Confidence Interval, Slope
Rules
Discrete Random Variables 51-75 Sample, Standard, Population, Distribution, Independent
AND Probability Distributions
Continuous Random 76-100 Sample, Regression, Yields, Interval, Class
Variables AND THE Normal
Distribution
Sampling Distributions AND 101-125 Standard, Sample, Population, Confidence Interval, Error
THE Central Limit Theorem
Point Estimation AND 126-150 Sample, Regression, Standard, Error, Researcher
Confidence Intervals
TOTAL 150 All questions include answers and detailed rationales
,Section A - Descriptive Statistics AND DATA Display
Q1.
A sample of 8 hourly wages (in dollars) has a mean of 22 and a median of 25. If the largest
observation increases by 10 while all others stay the same, which statement is correct?
A. Both the mean and median increase by B. The mean increases, but the median
10. stays at 25.
C. The median increases, but the mean D. Neither the mean nor the median
stays at 22. changes.
Correct: B - The mean increases, but the median stays at 25.
Rationale:The mean is sensitive to every observation, so raising the largest value by 10
raises the mean by 10/8 = 1.25. The median depends only on the middle order statistics,
which are unaffected when the largest value increases. Thus the mean rises while the median
remains 25.
Why the other answers are wrong:
A. The median is a positional measure and does not respond to changes in the extreme value.
C. The mean is not robust to outliers, so it must change when an observation changes.
D. The mean necessarily responds to any change in an observation's value.
Reference: Stock & Watson, Introduction to Econometrics, 4th Ed., Ch. 3 (Measures of Location)
Q2.
In a survey of UCLA economics majors, 60% have taken calculus, 50% have taken
statistics, and 30% have taken both. Given a randomly selected student has taken
statistics, what is the probability they have also taken calculus?
A. 0.30 B. 0.50
C. 0.60 D. 0.80
Correct: C - 0.60
Rationale:By definition of conditional probability, P(Calculus | Statistics) = P(both) /
P(Statistics) = 0..50 = 0.60. The joint probability is divided by the conditioning event's
marginal probability.
Why the other answers are wrong:
A. 0.30 is the joint probability P(both), not the conditional probability requested.
B. 0.50 is P(Statistics) alone and ignores the conditioning information.
D. 0.80 would result from an incorrect operation such as 0.30 + 0.50.
Reference: Ross, A First Course in Probability, 10th Ed., Ch. 3 (Conditional Probability)
Page 3
, Section A - Descriptive Statistics AND DATA Display
Q3.
A random variable X has E[X] = 4 and Var(X) = 9. Define Y = 2X 5. What are E[Y] and
Var(Y)?
A. E[Y] = 3, Var(Y) = 13 B. E[Y] = 3, Var(Y) = 36
C. E[Y] = 8, Var(Y) = 18 D. E[Y] = 3, Var(Y) = 18
Correct: B - E[Y] = 3, Var(Y) = 36
Rationale:By linearity, E[Y] = 2E[X] " 5 = 2(4) " 5 = 3. Variance scales by the square of the
multiplicative constant: Var(Y) = 2² Var(X) = 4(9) = 36; additive constants do not affect
variance.
Why the other answers are wrong:
A. 13 incorrectly adds the constant 5 to the variance instead of recognizing Var is invariant to
shifts.
C. 8 mistakenly uses E[X] = 4 without applying the transformation to the mean.
D. 18 incorrectly scales variance by 2 rather than 2².
Reference: Wackerly et al., Mathematical Statistics with Applications, 7th Ed., Ch. 3 (Expected Value)
Q4.
The number of defective microchips in a batch of 20 follows a binomial distribution with n
= 20 and p = 0.05. Which expression gives P(X = 2)?
A. C(20,2)(0.05)²(0.95)¹ B. C(20,2)(0.05)¹(0.95)²
C. (0.05)²(0.95)¹ D. C(20,2)(0.05)²(0.95)²
Correct: A - C(20,2)(0.05)²(0.95)¹
Rationale:The binomial pmf is P(X = k) = C(n,k) p^k (1"p)^(n"k). With n = 20, k = 2, p = 0.05,
this yields C(20,2)(0.05)²(0.95)¹, where the binomial coefficient counts the ways to choose
which 2 chips are defective.
Why the other answers are wrong:
B. The exponents on p and (1p) are swapped; p must be raised to the number of successes k =
2.
C. Omits the binomial coefficient C(20,2) that counts the arrangements of the two successes.
D. Uses exponent 20 on (0.95) instead of n k = 18.
Reference: Newbold et al., Statistics for Business and Economics, 9th Ed., Ch. 4 (Binomial Distribution)
Q5.
A continuous random variable X has density f(x) = kx on the interval [0, 2] and 0
elsewhere. What is the value of k?
Page 4
