Statistics 1

Attachments:

• Discrete Random Variables quick quiz

1. Probability Distributions
   1. E(X) = μ

      Annotations:

      • Σxp multiply each value of x by its corresponding probability, then sum
   2. Var(X)

      Annotations:

      • Σx^2 * p - μ^2 Square each value of x, multiply by corresponding probablity, sum and subtract μ^2
2. Geometric Distribution
   1. X~Geo(p)
   2. Keep going until a success
   3. P(X=x)

      Annotations:

      • P(X=x) = (1-p)^(x-1) * p x=1,2,3...
   4. E(X)

      Annotations:

      • E(X) = 1/p
   5. P(X>x)

      Annotations:

      • P(X>x) is the same as (1-p)^x 
3. Binomial Distribution
   1. X~B(n,p)

      Annotations:

      • n number of events, p probability of success
   2. P(X=x)

      Annotations:

      • P(X=x)= nCx * p^x * (1-p)^(n-x) x+0,1,2... n
   3. E(X)

      Annotations:

      • E(X) = np
   4. Var(X)

      Annotations:

      • Var(X) = np(1-p)