Summary 2DD80 statistics for industrial engineering

2DD80
Statistics for IE


Chapter 4: continuous random variables and probability distributions
4.1: probability distributions and probability density functions
Continuous random variable = random variable with an interval (either finite or infinite) of real
numbers for its range
A probability density function f(x) can be used to describe the probability distribution of a
continuous random variable X. The probability that X is between a and b is determined as the
integral of f(x) from a to b.




A histogram is an approximation to a probability density function. For each interval of the
histogram, the area of the bar equals the relative frequency of the measurements in the
interval. The relative frequency is an estimate of the probability that a measurement falls in the
interval.




4.2: cumulative distribution functions

,In the definition of F(x), any < can be changed to ≤ and vice versa.




4.3: mean and variance of a continuous random variable

,4.4: continuous uniform distribution




The expected value of X and the variance of X are:

, 4.5: normal distribution




P(μ – σ < X < μ + σ) = 0.6827
P(μ – 2σ < X < μ + 2σ) = 0.9545
P(μ – 3σ < X < μ + 3σ) = 0.9973




From the symmetry of P(X < μ) = P(X > μ) = 0.5