Question 1
Bernoulli vs Binomial (setup + use cases)
- Bernoulli: one trial, X∈{0,1}, parameter p. \(P(X=1)=p\), \(P(X=0)=1-p\).
- Binomial: number of successes in n independent Bernoulli trials. \(X \sim \mathrm{Bin}(n,p)\), \(\mathbb{E}[X]=np\), \(\mathrm{Var}(X)=np(1-p)\).
- Use: Bernoulli = single default/click; Binomial = number of defaults in n loans.