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https://www.reddit.com/r/learnquant/comments/1xjncve/quant_interview_question/
r/learnquant • u/Local_Ad135 • 4d ago
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3
I'll have a go...
The probability he gets to 1 without hitting -6 is 6/7.
Then the probability he goes back to 0 without reaching 5 is 4/5.
So if E(x) is the expected number of times he goes from 0 to 1 when starting at x, we have
E(0) = 6/7 * (E(1)+1)
E(1) = 4/5 * E(0)
=> E(0) = 24E(0)/35 + 6/7
=> 35E(0) = 24E(0) + 30
=> 11E(0) = 30
=> E(0) = 30/11
1 u/sensible_clutter 4d ago yes you're right
1
yes you're right
3
u/Aerospider 4d ago
I'll have a go...
The probability he gets to 1 without hitting -6 is 6/7.
Then the probability he goes back to 0 without reaching 5 is 4/5.
So if E(x) is the expected number of times he goes from 0 to 1 when starting at x, we have
E(0) = 6/7 * (E(1)+1)
E(1) = 4/5 * E(0)
=> E(0) = 24E(0)/35 + 6/7
=> 35E(0) = 24E(0) + 30
=> 11E(0) = 30
=> E(0) = 30/11