Geometric Distribution

• Definition: Number of trials needed to get the first success in independent Bernoulli trials with success probability $p$
• Mean: $E[X]=\frac{1}{p}$
• Variance: $Var(X)=\frac{1-p}{p^2}$
• Use case: Models waiting time until first success (first heads in coin flips).

Represented as $\mathrm{Geometric}(p)$

Mathematically as $P(X=k)=(1=p{)}^{k-1}p$

Visually as