Free FRM Quantitative Analysis Practice Questions & Answers
400 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 start
Question 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.
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?
Every question on this page stays free and open either way.
Add Your Testimonial
Privacy Preference
We use cookies to enhance your browsing experience, serve personalized content, and analyze our traffic. By clicking "Accept All", you consent to our use of cookies on this platform.
Before you go, can we ask you one thing?
We are just getting started, and knowing what is holding you back would help us a lot. It takes about 20 seconds.
Overall rating
★★★★★
How likely are you to recommend us to a friend? (0 to 10)What is stopping you from creating a free account?
🎉
Thank you
We read every response. This is exactly how we make PCC better for you.
CCarr
Free assistant · no signup
Carr only reads what is public on PCC, plus your own practice progress.