unit 6

lesson 1

• discrete random variable → takes a fixed number of values with gaps between values

lesson 2

• SD² = variance

• use normalcdf to find area under the curve

lesson 3

• addition and subtraction to a distribution → mean changes, SD stays the same

• multiplication and division to a distribution → both mean and SD change

lesson 4

• combining random variables

  • M_X+Y = M_X + M_Y, SD_X+Y = sqrt(SD_X² + SD_Y²)

  • M_X-Y = M_X - M_Y, SD_X-Y = sqrt(SD_X² + SD_Y²)

  • you can’t just add standard deviations

lesson 5

• binomial distribution ( x → number of successes)

• BINS

  • B → binary (success or failure)

  • I → independent trials

  • N → number of trials is fixed (n)

  • S → same probability of success

• binomial formula

  • P (x = k) = _nC_k*p^k(1-p)^n-k

    • _nC_k → number of ways to get k successes

    • p → probability of success

    • k → # of successes

    • (1-p) → probability of failure

    • n-k → number of failures

lesson 6

• mean for binomial distribution → M = np

  • “after many, many groups of [n] trials, the average number of successes is [M].”

• standard deviation for binomial distribution → SD = sqrt(np(1-p))

  • “the number of successes typically varies by [SD] trials from the mean of [M].”

lesson 7

lesson 8

• geometric distribution

• BITS

  • B → binary (success or failure)

  • I → independent trials

  • T → trials until success

  • S → same probability of success

• P(x=k) = (1-p)^k-1 * p

  • (1-p) → probability of failure

  • k → # of failures

  • p → probability of success

• geometric distribution description

  • shape → skewed right

  • center → M = 1/p

  • variability → SD = sqrt(1-p)/p