Your question is Validate a Probability Distribution. Take a moment with it on the right.
Talk me through your thinking if you like. When you're confident, submit your answer and I'll grade it like a real screen (7/10 or better passes).
A different desk at DRW Holdings models round-trip order latency, rescaled to x in [0, 1], and proposes the candidate density and derivation below.
Candidate density:
f(x) = 4x(1 - x), for x in [0, 1]
f(x) = 0, otherwise
Claimed CDF (their derivation, handed to you alongside f):
F(x) = 2x^2 - x^3, for x in [0, 1]
Their note: "f is symmetric around x = 0.5 and f(0) = 0, so we take that
to mean zero-latency round trips never happen in this model."
Verify whether f is a valid probability density function, check their derivation of F, and evaluate their closing claim about f(0) = 0.