Statistics Chapter 5: Continuous Random Variable

Continuous random variable

can assume any numerical value within some interval or intervals

Ex: Randomly choose a battery from a production line and record its lifetime

Probability Distributions for Continuous Random Variables

• the graph of the probability distribution is a smooth curve called: probability density function (f(x))

• there are an infinite number of outcomes

Mean of a numerical variable x (μ)

describes where the probability distribution of x is centered

Interpretation: if you randomly pick…, then in the long run, on average, the….will be μ = …

Standard deviation of a numerical variable x (σ)

describes variability in the probability distribution

1. When σ is close to 0, observed values of x will tend to be close to the mean value

2. When σ is large, there will be more variability in observed values

The Uniform Distribution

x can take on any value between c and d with equal probability