easy Probability
A release-checked easy problem for training Conditional Expectation, Coins, Geometric/Negative Binomial, Markov Chains.
A coin with probability $0 < p < 1$ of heads per flip is repeatedly flipped. A run is defined as a maximal sub-sequence of the same outcome. For example, the sequence $HHHTHTTTT$ has $4$ runs: $HHH, T, H,$ and $TTTT$. Find the expected length of the first run when $p = 1/3$.
This Probability problem is tagged Conditional Expectation, Coins, Geometric/Negative Binomial, Markov Chains. State the random variables and conditioning information explicitly, then check the result against boundary cases before opening hints or a solution.
Probability · Akuna
Probability
Probability
Probability · SIG, DE Shaw
Probability · SIG, Jane Street
Probability · Jane Street