• Bernoulli Distribution: This is the simplest case where there is a single trial with a binary outcome (success or failure). Bernoulli distribution models individual trial outcomes and gives probability
  • p for X=1
  • 1-p for X=0
• Binomial Distribution: Multiple Bernoulli trials form a binomial distribution. This is crucial for calculating confidence intervals for proportions because it allows for the aggregation of multiple trials to estimate the population proportion more accurately. It gives probability for k success in n trials assuming single trial probability is p. Example
  • probability of 10 success in 100 trials with p=0.4

Bernoulli distribution

• Has 2 Possible Random Variables: 0 & 1 where 1 is success and 0 is failure (Example: 1 coin toss)
  • P(1)=p (Example: coin toss 0.5 probability for getting heads)
  • P(0)=1-p
• EX=p
• DX=p(1-p)
• STD=$\sqrt{p(1-p)}$

Example of Bernoulli distribution

How std varies with different p values

• p=0.5 , highest deviation

Binomial distribution