De nition 4.1.2: Probability Density Function (PDF) dom variable (one whose range is typically an interval or union of i tervals). The probability density function fX(z) 0 for all z 2 R • 1 fX(t) dt = 1

CDF: The cdf of a normal random variable does not exist in closed form. Probabilities involving normal random variables and normal quantiles can be computed numerically.

Know the definition of a continuous random variable. Know the definition of the probability density function (pdf) and cumulative distribution function (cdf). Be able to explain why we use probability …

Note: The above calculation also says that for a continuous random variable, for any fixed number a, the probability the random variable takes the value exactly equal to a, namely P(X = a) = 0!

In principle variables such as height, weight, and temperature are continuous, in practice the limitations of our measuring instruments restrict us to a discrete (though sometimes very finely subdivided) world.

Chapter 5 Understanding Chapter 5 goals: After this chapter, you should be able to understand: (1) The definition and properties of a continuous random variable; (2) The Uniform Distribution; (3) The …

Another important way of representing a continuous probability distribution is the prob-ability density function or pdf. This is actually the gradient of the distribution function.