1-exploring Random Variables.pptx

Random Variables and Probability Distribution

How do we use the concept of Probability in making decision?

Decision Making an important aspect in business, education, insurance, and other real-life situations.  Many decisions are made by assigning probabilities to all possible outcomes pertaining to the situation and then evaluating the result. 

Lesson 1 Exploring Random Variables

Sample Space - The set of all possible outcomes of an experiment.

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Review

ENTRY CARD

List the sample space of the following experiment. Experiment

Tossing three coins Rolling a die and tossing a coin simultaneously Drawing a spade from a deck of cards Getting a defective item when two items are randomly selected from a box of two defective and three nondefective items. Drawing a card greater than 7 from a deck of cards.

Sample space

Halimbawa Suppose three cell phones are tested at random. We want to find out the number of defective cell phones that occur. Thus, to each outcomes in a sample space we shall assign a value. These are 0, 1, 2, 3, If there is no defective cell phone, we assign the number 0; if there is 1 defective cellphone, we assign the number 1; if there are two defective cell phones, we assign the number 2; and 3, if there are three defective cell phones. The number of defective cell phones is a random variable. The possible values of this random are 0, 1, 2, and 3.

Activity1: Tossing three coins Suppose three coins are tossed. Let Y be the random variable representing the number of tails that occur. Find the values of the random variable Y. Complete the table.

Activity 2: Drawing Balls from an Urn

Two balls are drawn in succession without replacement from an urn containing 5 red balls and 6 blue balls. Let Z be the random variables representing the number of blue balls. Find the values of the random variable Z. Complete the table below.

Discrete Random VariableThe set of possible outcomes are countable. Continuous Random Variable – If it takes on values on continuous scale. Hal. Heights, weights and temperature.

Lesson 2. Constructing Probability Distributions ENTRY CARD

Event (E) Getting an even number in a single roll of a die Getting the sum of 6 when two dice are rolled Getting an ace when a card is drawn from a deck. Probability that all children are boys if a couple has three children Getting odd number and a tail when a die is rolled and a coin is tossed simultaneously Getting the sum of 11 when two dice are rolled Getting a black card and a 10 when a card is drawn from a deck Getting a red queen when a card is drawn from a deck. Getting doubles when two dice a rolled Getting a red ball from a box containing 3 red and 6 black balls

Probability P(E)

Halimbawa 1. Suppose three coins are tossed. Let Y be the random variable representing the number of tails that occur, Find the probability of each values of random variable Y.

Halimbawa 2 Two balls are drawn in succession without replacement from an urn containing 5 red balls and 6 blue balls. Let Z be the random variable representing the number of blue balls. Construct the probability of the random variable Z.

Halimbawa 3. Suppose three cell phones are tested at random. Let D represent the defective cell phone and let N represent the non- defective cellphone. If we let X be the random variable from the number of defective cell phones, construct the probability distribution of the random variable X

Properties of a Probability Distribution  The

probability of each value of the random variable must be between or equal to 0 and 1. Or 0 ≤ 𝑃(𝑥) ≤ 1.  The sum of the probabilities of all values of the random variable must be equal to 1 or σ 𝑃 𝑥 = 1.

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