Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 320 / 1 / c

Solution

At fixed intrinsic ratio

q

, part a gives

Q^{2} = q^{2} + (1 - q^{2}) μ^{2}, μ = \frac{Q ^{2} - q ^{2}}{1 - q ^{2}} .

Since

μ

P (Q ∣ q) = \frac{d μ}{d Q} = \frac{Q}{1 - q ^{2} Q ^{2} - q ^{2}}, q \leq Q \leq 1 .

Q = q

is integrable, and direct integration gives one.

There are no discussions about this article yet.

There are currently no matching articles.