← Point72 Asset Management Interview Insights
My first instinct was to set up an integral and I immediately started second-guessing myself on the bounds.
Recognize that X - 3Y is a linear combination of independent normals, hence normally distributed with mean 0 and variance 10. Then compute P[X - 3Y > 0] = 1/2 by symmetry, and explain the reasoning clearly.
Pro tip: Emphasize that the result is exactly 1/2 due to symmetry, not an approximation, and connect it to the fact that any symmetric continuous distribution has equal probability above and below its mean.
Rewrite the inequality as X - 3Y > 0 to simplify the comparison.
Since X and Y are independent normal, X - 3Y is also normal. Compute its mean and variance: mean = 0, variance = 1 + 9 = 10.
A normal distribution is symmetric about its mean, so P[X - 3Y > 0] = P[X - 3Y < 0] = 1/2.
State the final answer as 1/2, and optionally verify by standardizing or noting that the probability does not depend on the variance.
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