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Annotated Sampling and Distribution

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Distributions, Sampling and Estimation

Our main objective in this section is to learn how to estimate some important characteristics of random variables using data. We will concentrate on estimating the mean from a normal distribution, and the proportion of success in a binomial distribution. To talk about estimation, we first need to know something about distributions and sampling.

Most data used for decision making exhibit variation. We are interested in drawing conclusions from such data. Probability and statistics give us the necessary tools.

We will again make use of the concept of a random variable. We have reviewed discrete random variables already. Before moving on, we need to review continuous random variables.

Continuous random variables take on continuous or interval values (there are an infinite number of possibilities). If you are measuring, the distribution of the result will almost always be continuous. For example, the width of an extruded bar is a continuous random variable.

The distribution of a continuous random variable is represented by a continuous curve (called the probability density function (pdf) and often denoted f(y)). The height of the curve does not represent probabilities; instead, the area under the curve between two points tells us about the probability. As a result, the probability that a continuous random variable is exactly equal to a single value is 0 (there is no area under a single point).

The Binomial and Normal Distributions

As noted earlier, we will be talking about estimating the mean of a normal distribution and the proportion of success in a binomial distribution. To proceed, therefore, we need to review these two distributions.

The Binomial Distribution

The binomial distribution is a discrete distribution and

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