Concepts4

Linearity of Expectation Applications

Linearity of expectation says the expected value of a sum equals the sum of expected values, even if the variables are dependent.

#linearity of expectation#indicator variables#expected inversions+12

∑MathIntermediate

Expected Value

Expected value is the long-run average outcome of a random variable if you could repeat the experiment many times.

#expected value#linearity of expectation#indicator variables+12

⚙️AlgorithmIntermediate

Randomized Algorithms

Randomized algorithms use coin flips (random bits) to guide choices, often making code simpler and fast on average.

#randomized algorithms#las vegas#monte carlo+12

⚙️AlgorithmAdvanced

DP with Expected Value

Dynamic programming with expected value solves problems where each state transitions randomly and we seek the expected cost, time, or steps to reach a goal.

#expected value dp#linearity of expectation#indicator variables+11