Expected values

• DRVs:

  E(X) = sum of x*p
• DRVs:

  Var(X) = E(X^2) - E(X)^2
• DRVs:

  Mode = value of X with greatest probability
• DRVs:

  Median = P(X=<M) = 0.5

  P(X=>M) = 0.5
• DUDs:

  E(X) = (n+1)/2
• CRVs: E(X) = ∫ x*f(x)​ dx

  Limits are -infinity and infinity
• CRVs: E(X^2) = ∫ x^2*f(x)​ dx

  Limits are -infinity and infinity
• CRVs:

  Var(X) = E(X^2) - E(X)^2
• CRVs:

  Lower quartile Q1 =CRVs: ∫ f(x) dx = 1/4

  Limits are -infinity and Q1

  
  

  Median [M] would be between -infinity and M, and would be equal to 1/2
• CRVs:

  E(aX + b) = aE(X) + b

  Var(aX + b) = a^2Var(x)
• DUDS:

  Var(X) = (n-1)(n+1)/12
• DRVs:

  E(X^-2) = $\sum$ 1/x^2 * P(X=x)