statistics

Mean (Expected Value) Of A Geometric Random Variable；binomial and geometric random variables。

statistics

• binomial and geometric random variables
  • mX = np s X = np(1- p)
• The Large Counts Condition
  • use the Normal approximation when n is so large that np ≥ 10 and n(1 – p) ≥ 10
    • mX
    • = np
• Mean (Expected Value) Of A Geometric Random Variable
  • 子主题
    • f Y is a geometric random variable with probability p of success on each trial,
    • then its mean (expected value) is
    • E(Y) = µY= 1/p.
• geometric settings
  • In a binomial setting, the number of trials n is fixed and the binomial random variable X counts the number of successes
• geometric random
  • In a geometric setting, if we define the random variable Y to be the number of trials needed to get the first success,
• geometric distribution.
  • . The probability distribution of Y
• the same
• one success
• independent