F.M Stats

• discrete uniform distribution Variance 


  (n²-1)/12
• Poisson Distribution


  X ~ Po(λ)

  where λ is the mean

  where δ is the standard deviation, sqrt λ
• Discrete Random Variable

  Expectation

  Expectation of X is equal to the sum of the values multipled by their probabilities

  
• Discrete Random Variable

  Expectation of X²

  The Expectation of X² is equal to the sum value squared multiplied by the probability of the value

  
• Variance of X


  Variance of X is equal to the Expectation of X² minus the (Expectation of X)²

  
• Cumulative Random Variable

  CRV is equal to the integration of ((x) multiplied by the function)

  
• Cumulative Random Variable

  Expectation of X²

  Expectation of X² is equal to the integration of ((X²) multiplied by the function)
• Cumulative Random Variable

  Finding the mode


  Mode means the point with the most, find turning point and then draw graph, find the highest position on the

  f'(x)=0
• Cumulative Random Variable

  Median


  Median => middle of the data, halfway between the data

  Probability = 1/2

  integration = 1/2
• Discrete Uniform Distribution

  Probability of x

  P(X=x) = 1/n

  where n is the highest value
• Discrete Uniform Distribution

  Expectation


  E(X)=(n+1)/2

  expectation is the mean
• Discrete Uniform Distribution

  Variance


  Var(X)=(n²-1)/12
• How is Discrete Uniform Distribution modelled?

  X ~ U(n)
• How is Poisson Distribution modelled?

  X ~ Po (λ)
• Poisson Distribution Probability

  P(X=x) = [e^(-λ) × λ^(x)]/x!
• Sum of independent Poisson Distribution

  Z ~ Po (λ + μ)
• Type I error

  Ho rejected when true
• Type II error

  Ho accepted when false
• Continuous Random Variable

  Linear Transformations

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

  Var(aX+b) = a²Var(X)
• Random Variables

  E(X+Y) = E(X) + E(Y)

  Var(X+Y) = Var(X) + Var(Y)
• Confidence Interval for Population Mean μ

  x(bar) +/- Z×σ/(sqrt n)
• width of a confidence interval


  2Z × σ/(sqrt n)