FRM Part I · FRM Exam Part I · Fundamentals of Probability
A random variable X has E[X] = 4 and E[X^2] = 25. Variable Y is defined as Y = 3 - 2X. What is the variance of Y?
The variance of Y is 36. Variance of X is 25 minus 16, which is 9. Since Y = 3 - 2X, the constant shift is irrelevant and the slope is squared, so the variance is 4 times 9, giving 36.
- A36Correct
- B18
- C9
- D81
Explanation
Var(X) = E[X^2] - (E[X])^2 = 25 - 16 = 9. Var(Y) = (-2)^2 × 9 = 36. The constant 3 does not affect variance. Answering 18 comes from multiplying by 2 instead of squaring the coefficient, and 9 ignores the scaling.
Did you get it right without looking?
One question tells you little. A timed set on Fundamentals of Probability shows your real accuracy, how long you take and where you lose marks.
More Fundamentals of Probability questions
- A bank's fraud model flags a transaction as suspicious. Historically, 2% of transactions are fraudulent. The model flags 90% of fraudulent t…
- Which statement about expectations of random variables X and Y is correct in general?
- A continuous random variable X has CDF F(x) = 0 for x < 0, F(x) = x^2/4 for 0 ≤ x ≤ 2, and F(x) = 1 for x > 2. A risk analyst wants the 75th…
- Two counterparties default independently over one year with probabilities 4% and 10%. Given that at least one of them defaults, what is the …
- X has E[X] = 4 and E[X^2] = 25. What is Var(X)?
- A risk analyst classifies next quarter's outcomes for a loan portfolio into three events: A = 'default losses below 1%', B = 'default losses…