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  • STA256 Lecture 17

Bernoulli Distribution

• Discrete
• Models the probability of observing a success or failure on 1 trial
• Probability Mass Function:
• $P(X=x)=p^x(1-p{)}^{1-x}x=0,1$
• $p$ is the probability of success
• $1-p$ is the probability of failure
• $x$ is number of success
• $1-x$ is number of failures
• Properties:
  • Mean: $\mu =E(X)=p$
  • Variance: ${\sigma }^2=var(x)=p(1-p)$
• Example:
  • Tossing a coin just once and observing heads
  • Rolling a die just once and observing number $3$