yr1 chap 6 statistical distributions

• the rules for when you can use a binomial distribution are:

  • fixed number of trials
  • two possible outcomes
  • fixed probability of success
  • trials are independent of each other
• for X $\sim$B(n,p):

  n is the number of trials

  p is the probability of success

  1-p is the probability of failure
• to find the probability of an exact number of successes:

  use BPD(X, n, p)
• to find the probability of an exact or less than number of successes:

  use BCD(X, n, p)
• to find the probability of an exact or greater than number of successes:

  think that P(X $\ge$ Y) is the same as 1 - P(X $\le$Y-1)

  use 1 - BCD(X-1, n, p)
• to find the probability of a specific range of number of successes:

  think that P(Y$\le$X$\le$Z) is the same as P(X $\le$Z) - P(X $\le$Y)

  use BCD(Z, n, p) - BCD(Y-1, n, p)
• if a question asks you to write down the probability distribution, it means draw a table with two rows, one labelled x and one labelled P(X = x), and fill in each possible value of x and the corresponding probability