IBDP Mathematics Analysis & Approaches HL Chapter 12 Notes

Probability Distributions

STUDY NOTES FOR MATHEMATICS – CHAPTER 12 – Probability Distributions

All DP mathematics courses serve to accommodate the diverse range of needs, interests and abilities of students, and to fulfill the requirements of various university and career aspirations. The aims of these courses are to enable students to: develop mathematical knowledge, concepts, principles, logical, critical and creative thinking, employ and refine their powers of abstraction and generalization. Students are also encouraged to appreciate the international dimensions of mathematics and the multiplicity of its cultural and historical perspectives.

Variables usually depend on chance events. As a result, we cannot predict the exact value they will take when we measure them next. However, we can determine the possible values the variables could take, and assign the probability of it occurring to each value. In this chapter, we use probability to to model the random variation or distribution of numerical variables. We learn about the different types of variables such as random, discrete random and continuous random. For each of these variables, there is a corresponding probability distribution which describes the probability that the variable will take a particular value. In addition to mean, we also learn to calculate the variance and standard deviation of a discrete random variable. Furthermore, this chapter deals with the various types of distribution, such as binomial, poisson distribution and how we can use technology to solve them.
In this chapter, we consider the variables with symmetrical, bell-shaped distribution curves. We call this a normal distribution. This happens to be the most important distribution in statistics. The normal distribution arises in nature when many different factors affect the value of the variable. Some examples of quantities that may be normally distributed or approximately normally distributed are: the heights of 15 year old girls, the volumes of liquid in soft drink cans, the length of adult sharks, etc. The exact location and shape of the curve is determined by the mean which measures the centre of the distribution, and the standard deviation which measures the speed of the distribution. We then later calculate probabilities using normal distribution.