Random Variable and Probability Distribution.pptx
- 1. LESSON 1 Random Variable and Probability Distribution
- 2. Learning Objectives illustrates a random variable (discrete and continuous) distinguished between a discrete and a continuous random variable finds the possible values of a random variable illustrates a probability distribution for a discrete random variable and its properties computes probabilities corresponding to a given random variable
- 4. Experiments are any movement or activity which can be done repeatedly under similar or comparative condition.
- 5. Outcomes are the result of a given experiment
- 6. Sample Space is the set of all possible outcomes of an experiment
- 7. Example rolling a die (dice) is an example of experiment
- 8. Example Upon rolling the die, it is expected that it will show a dot on the top which are either 1, 2, 3, 4, 5 or 6, these are what we call the sample space of the given experiment. If you are only interested on a given value of dots, let say, three dots, then “3” is what we call the outcome or the sample.
- 9. is a characteristic or attribute that can assume different values (ex. in algebra, variables like x can be any number) use capital letter (X, Y, Z, and others) to denote or represent a variable.
- 10. Example 1: TOSSING THREE COINS Suppose you have three coins. We want to find the number of heads that will occur after tossing the coins. To determine the number of sample space, we are going to use the basic probability rule. Since there are three coins, and each coin will give us 2 outcomes, then n(S) = 2.2.2 = 23 = 8 possible outcomes or sample space.
- 11. TREE DIAGRAM
- 13. Random Variable is a capacity that connects a real number withevery component in the sample space
- 14. Random Variable It is a variable whose qualities are controlled by chance.
- 15. Example 2: BOYS or GIRLS? An experiment consists of studying the number of boys in families with exactly 2 children. The random variable X may be used to represent the number of boys.
- 17. Sample space = 4 possible outcomes Random Variable : X = {0,1,2}
- 18. Example 3: DEFECTIVE or NON- DEFECTIVE Suppose 4 laptops are tested at random. Let N represent the non- defective laptops and let D represent the defective laptops. If we let Z be the random variable for the number of non-defective laptops, determine the value of the random variable Z.
- 19. Solution: Based on the given problem, there are 4 laptops that we will be tested at random and each laptop can either be defective or non-defective. Let us first determine the number of sample space. Since there are 4 laptops and each laptop can be defective or non- defective, then n(S) = (2)(2)(2)(2) = 24 = 16 sample space / possible outcomes.
- 21. From the table, the values of the random variable Z are 0, 1, 2, 3, and 4. This means that it is possible that out of the 4 laptops you will have, there can be 0, 1, 2, 3, or 4 non-defective. It can also be observed that no number is greater than 4
- 22. TYPES OF RANDOM VARIABLE Discrete Random Variables are variables that can take on a finite number of distinct values. In easier definition, discrete random variable is a set of possible outcomes that is countable.
- 23. TYPES OF RANDOM VARIABLE Discrete Random Variables Examples number of heads acquired while flipping a coin three times the number of defective chairs, the number of boys in the family, the number of students present in the online class
- 24. TYPES OF RANDOM VARIABLE Continuous Random Variables are random variables that take an infinitely uncountable number of potential values, regularly measurable amounts.
- 25. TYPES OF RANDOM VARIABLE Continuous Random Variables Examples represent measured data, such as height, weights, temperature.