Continuous uniform distribution

• How do you calculate the probability that X takes a value to the nearest whole number?

  By calculating P(3.5 < X < 4.5)
• What is a continuous uniform distribution?

  All values in a range are equally likely

  
• What shape represents the probability density function (pdf) of a continuous uniform distribution?

  A rectangle
• How is a continuous uniform distribution denoted?

  X ~ U[a,b]
• What is the probability over the interval [a, b] in a continuous uniform distribution?

  It is constant and zero elsewhere
• How do you calculate probabilities using the continuous uniform distribution?

  Find the width of the interval and divide

  
• What is the formula for the pdf of a continuous uniform distribution?

  f(x) = 1/(b-a) for a ≤ x ≤ b
• What must the area under the rectangle equal in a probability distribution?

  It must equal 1
• How do you find the value of k in a continuous uniform distribution?

  Set the area equal to 1
• What is the mean of a continuous uniform distribution?

  E(X) = (a + b) / 2

  
• What is the variance of a continuous uniform distribution?

  Var(X) = (b - a)² / 12
• How do you derive the variance from the endpoints a and b?

  Using the formula Var(X) = (b - a)² / 12
• Remember this CUD


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