Numerical outcomes of random processes, either discrete or continuous.
A random variable maps outcomes to numbers. Discrete ones have a probability mass function; continuous ones have a density function with area 1. The cumulative distribution function F(x)=P(X≤x) describes both.
The lifetime of a bulb is a continuous random variable.
Random variables turn uncertain outcomes into numbers, which lets you apply algebra and calculus to noise, loads and times.
Numerical outcomes of random processes, either discrete or continuous.
Random variables turn uncertain outcomes into numbers, which lets you apply algebra and calculus to noise, loads and times.
Discrete variables take countable values, such as counts. Continuous variables take values in an interval and are described by a density.
A function whose integral over an interval gives the probability of falling in that interval. Its value at a point is not a probability.
Typical applications include modelling the number of defects per panel as a discrete variable, representing measurement noise as a continuous variable and describing the arrival time of a customer at a service desk.
Study "Conditional probability and Bayes" first (topic 78 of 104 in Engineering Mathematics). It covers the groundwork this topic builds on.
PMF sums to one. PDF integrates to one. Percentiles come from the inverse CDF.
The lifetime of a bulb is a continuous random variable.
The next topic is "Expectation and variance", which builds directly on this one.
It is classed as Advanced in Engineering Mathematics (topic 79 of 104). It is an advanced topic. It assumes you are comfortable with the intermediate topics in Engineering Mathematics.
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