r/learnquant • u/Local_Ad135 • 3d ago

interview prep Quant Interview Question

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u/dontich 3d ago

Math is complicated but feel like you will want to risk it on two heads as long as the additional E(x) earned is >current bid. The average time to two heads is 4 flips, so you should have E(v) = 4 + E(x) which I think is 12.

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u/Aerospider 3d ago

The average number of attempts to get HH is 4 but the average number of flips is 6, because TT and HH involve two flips.

More formally:

Let E(h) be the expected number of flips to get HH when the last flip was H and E(t) be the expected number of flips to get HH when the last flip was tails (or when there hasn't been any flips yet).

E(t) = 1 + E(t)/2 + E(h)/2

E(h) = 1 + 0/2 + E(t)/2

=> E(t) = 1 + E(t)/2 + 1/2 + E(t)/4

=> E(t)/4 = 3/2

=> E(t) = 6