1 RANDOM VARIABLE Paul Jorel R Santos Random
1 RANDOM VARIABLE Paul Jorel R. Santos
Random Variable 1 In some experiments such as tossing a coin three times, rolling a die twice, drawing two balls from an urn and the like, few are not oftentimes concerned with every detail of the outcomes.
Random Variable 2 We are usually interested in some numerals associated with the outcomes. For instance, if a coin is tossed twice, the set of all possible outcomes (S) of the experiment is:
Random Variable If we are interested in the number of tails that came out in the experiment, then we can assign numbers 0, 1, and 2 for each of the 4 possible outcomes. Thus, we can write
Sample Space TT Number of Tails 2 TH 1 HT 1 HH 0
Definition • 2
Types of Random Variables 2 •
Types of Random Variables 2 •
Definition • 2
Definition • 2
Example 1 • 2
Example 1: Answer • 2
Practice Exercise 2
Practice Exercise 2 6. The number of bread baked each day. 7. The air temperature in a city yesterday. 8. The income of single parents living in Quezon City. 9. The weights of newborn infants. 10. The capacity (in liters) of water in a swimming pool.
Probability Distribution 1 In the experiment of tossing a coin twice, there are four possible outcomes namely: HH, HT, TH and TT. If X is a random variable representing the number of tails in the outcomes, then:
Probability Distribution
Definition 2 A discrete probability distribution is a table showing all the possible values of a discrete random variable together with their corresponding probabilities.
Properties of Discrete Probability Distribution • 2
Example 1 2 Is the distribution below a discrete probability distribution? 1 0. 12 2 0. 82 3 0. 06
Example 2 2 Write the probability distribution of a random variable R representing the number of red balls when 3 balls are drawn in succession with replacement from a jar containing 4 red and 4 blue balls. 0 1 2 3/8 3 1/8
Example 3 2 Box A and Box B both contain the number 1, 2, 3 and 4. Write the mass function and draw the histogram of the sum when one number from each box is taken at a time, with replacement.
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