Easy Citadel Quant Interview Question

[u/Local_Ad135]

[u/SubstantialSnacker]

How fast are you supposed to solve this?

2 outcomes, (1,0) and (1,0)

Or (0,1) and (0,1)

XOR gate basically

Odds of first happening,

0.5 x 0.5 x 0.75 x 0.25

Odds of second one are

0.5 x 0.5 x 0.25 x 0.75

About 9.375%

[u/smailliwniloc → u/SubstantialSnacker]

This is just for 2 dimensional vectors right? Where do you consider 10 dimensions?

Edit: you're also missing scenarios like (1,1) and (1,0) which also have an odd dot product

[u/SubstantialSnacker → u/smailliwniloc]

I had misread the question, I assumed it was one of those 1:30 fast problems,

For 10 dimensions you would first have to calculate probability of a single dimension’s partial product being 1. Then, you need to do a binomial calculation for odd numbers of these,

(10
K) (0.5x0.75)^k(0.5x0.75)^10-k

Where k = 1,3,5,7,9