Lesson 2: Review of basic concepts of probability theory
Basic probability rules Random variables and associate concepts Normal distributions
Chapter 2 (1-7), Chapter 3 (1-5, 10-11) and Chapter 4 (1-8) (1 8)
Replicate and complete all the classroom exercises. Print answers of 2.1 (b-c-d), 2.3 (b-c-d) and 2.4(b-c-d) in one (1) page.
Lesson 2 - Page 2
At the end of the lesson, you should be able to:
Define and apply the basic probability rules Describe the basic concepts related to random variables D ib th b i t l t dt d i bl Describe and use the properties of means and variances Recognize and understand the ...view middle of the document...
Usually we can have only sample values of the variables as our data. A random variable can (only) be described by its distribution that tells us the probabilities that the random variable will take certain (ranges of) values values. Distribution of a random variable can be approximated through observed values using histogram, frequency table or chart. Distribution of real random variables can also be approximated by theoretical distributions like normal, uniform, student, chi square, etc. Notational convention: Random events: A, B, C, etc.; random variables: X, Y, Z, etc.; Constants: a, b, c, etc.; random values: x, y, x, etc. Remarks: Given a random variable X, we may have many random events like (X = a), (X a), (a Gi d i bl X h d t lik ) ) ( X b) for any constants a and b. A random variable (in probability theory) corresponds to a population (in statistics) Only random events have probability. Random variables have distribution that can be characterized by parameters (like mean, variance) or functions (like cumulative, density or mass functions). In statistics, random variables correspond to populations and are referred to as variables. Their observed values are commonly stored in columns of data tables.
Lesson 2 - Page 5
Classroom exercise 2.1
Consider data from HBAT Case a)...