Free Questions › FRM › Quantitative Analysis
Free FRM Quantitative Analysis Practice Questions & Answers
387 exam-style Quantitative Analysis questions. Pick your answer, hit Check answer, and see the worked solution — free to start, no signup.
100% free · No login to startQuestion 1
The expected value of a discrete random variable is:
Select an option first.
Correct answer: B — The sum of each possible outcome multiplied by its probability
Explanation: B
Question 2
Variance measures:
Select an option first.
Correct answer: B — The average squared deviation of outcomes from the mean
Explanation: B
Question 3
The standard normal distribution has:
Select an option first.
Correct answer: B — Mean of 0 and standard deviation of 1
Explanation: B
Question 4
Covariance between two random variables measures:
Select an option first.
Correct answer: B — The direction and degree to which two variables move together
Explanation: B
Question 5
The correlation coefficient between two variables is:
Select an option first.
Correct answer: B — The covariance divided by the product of the standard deviations of each variable
Explanation: B
Get the full FRM question bank — free
Drop your email and we'll send you fresh FRM practice questions, fully worked solutions and exam-deadline reminders. No spam — unsubscribe in one click.
Want to save your score and take a full mock exam? Create a free account →
Question 6
A leptokurtic distribution compared to the normal distribution has:
Select an option first.
Correct answer: B — Fatter tails and a more peaked centre
Explanation: B
Question 7
Skewness of a distribution measures:
Select an option first.
Correct answer: B — The asymmetry of the distribution around its mean
Explanation: B
Question 8
The central limit theorem states that:
Select an option first.
Correct answer: B — The distribution of sample means approaches normality as sample size grows, regardless of the underlying distribution
Explanation: B
Question 9
A 95% confidence interval means:
Select an option first.
Correct answer: B — If the same procedure is repeated many times, 95% of such intervals would contain the true parameter
Explanation: B
Question 10
A Type I error in hypothesis testing is:
Select an option first.
Correct answer: B — Rejecting a true null hypothesis
Explanation: B
Question 11
The p-value in hypothesis testing represents:
Select an option first.
Correct answer: B — The probability of obtaining a test statistic as extreme or more extreme than observed, assuming the null hypothesis is true
Explanation: B
Question 12
The Binomial distribution describes:
Select an option first.
Correct answer: B — The number of successes in a fixed number of independent Bernoulli trials with constant success probability
Explanation: B
Question 13
The Poisson distribution is commonly used to model:
Select an option first.
Correct answer: B — The number of rare events occurring in a fixed time period
Explanation: B
Question 14
A probability distribution is said to have fat tails when:
Select an option first.
Correct answer: B — There is a higher probability of extreme outcomes than a normal distribution would predict
Explanation: B
Question 15
The coefficient of variation (CV) measures:
Select an option first.
Correct answer: B — Relative volatility: standard deviation divided by the mean
Explanation: B
Question 16
The 95th percentile of a normal distribution is approximately how many standard deviations above the mean?
Select an option first.
Correct answer: B — 1.645
Explanation: B
Question 17
Two events A and B are mutually exclusive if:
Select an option first.
Correct answer: B — P(A ∩ B) = 0
Explanation: B
Question 18
The geometric mean return is used rather than the arithmetic mean for:
Select an option first.
Correct answer: B — Multi-period compounding — it correctly represents the compound growth rate over multiple periods
Explanation: B
Question 19
The probability that a random variable X falls within k standard deviations of its mean, for any distribution with finite mean and variance, is at least:
Select an option first.
Correct answer: B — 1 - 1/k² (Chebyshev's inequality)
Explanation: B
Question 20
If X and Y are independent random variables, then:
Select an option first.
Correct answer: B — Cov(X,Y) = 0 and Var(X+Y) = Var(X) + Var(Y)
Explanation: B
Question 21
The median of a distribution is:
Select an option first.
Correct answer: B — The value that divides the distribution into two equal halves
Explanation: B
Question 22
The sample variance is calculated using n-1 in the denominator (rather than n) in order to:
Select an option first.
Correct answer: B — Produce an unbiased estimator of the population variance (Bessel's correction)
Explanation: B
Question 23
The cumulative distribution function (CDF) F(x) gives:
Select an option first.
Correct answer: B — The probability that X is less than or equal to x: P(X ≤ x)
Explanation: B
Question 24
If X ~ N(0, 1), then X² follows:
Select an option first.
Correct answer: B — Chi-squared distribution with 1 degree of freedom
Explanation: B
Question 25
In risk management, the 99th percentile loss over one day is:
Select an option first.
Correct answer: B — The loss that will not be exceeded on 99 out of 100 trading days (equivalently, expected to be exceeded only 1% of the time)
Explanation: B
Question 26
The standard error of the sample mean is:
Select an option first.
Correct answer: B — σ / √n — the standard deviation of the sampling distribution of the mean, which decreases as sample size increases
Explanation: B
Question 27
The variance of a constant is:
Select an option first.
Correct answer: B — Zero — a constant has no variability
Explanation: B
Question 28
A fat-tailed distribution is described by:
Select an option first.
Correct answer: B — Excess kurtosis greater than zero (leptokurtic) — more probability mass in the tails than the normal distribution
Explanation: B
Question 29
The probability of A union B (A or B occurring) is:
Select an option first.
Correct answer: B — P(A) + P(B) - P(A ∩ B) — the inclusion-exclusion principle, subtracting the double-counted intersection
Explanation: B
Question 30
If X ~ N(10, 25), what is the probability that X exceeds 15?
Select an option first.
Correct answer: A — 15.87%
Explanation: A
More free FRM topics
Financial Markets and Products400
Operational Risk and Resilience400
Liquidity and Treasury Risk Management400
Credit Risk Measurement and Management399
Market Risk Measurement and Management398
Risk Management & Investment Management398
Foundations of Risk Management397
Valuation and Risk Models394
Ten questions in
- The ones you miss are saved as a drill you can repeat
- Your place is kept, on this device and any other
- A streak, if that is the thing that gets you back tomorrow
Every question on this page stays free and open either way.