Random Variable (Discrete and Continuous)
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The document discusses statistics and probability concepts, focusing on random variables which can be discrete or continuous. It defines statistical experiments, sample spaces, and provides examples of determining the nature of various random variables. The content is intended for educational purposes, targeting understanding of basic statistical principles.
Random Variable (Discrete and Continuous)
- 1. Statistics and Probability • PRINCESS P. DIPASUPIL • Special ScienceTeacher I Statistics and Probability • PRINCESS P. DIPASUPIL • Special ScienceTeacher I RandomVariable: Discrete & Continuous Statistics and Probability PRINCESS P. DIPASUPIL Special ScienceTeacher I
- 2. Statistics and Probability • PRINCESS P. DIPASUPIL • Special ScienceTeacher I STATISTICAL EXPERIMENT activity outcome/s any activity that produces outcomes
- 3. Statistics and Probability • PRINCESS P. DIPASUPIL • Special ScienceTeacher I a process that will generate data where the outcomes have a corresponding chance of occurrence. STATISTICAL EXPERIMENT
- 4. Statistics and Probability • PRINCESS P. DIPASUPIL • Special ScienceTeacher I SAMPLE SPACE the set of all possible outcomes
- 5. Statistics and Probability • PRINCESS P. DIPASUPIL • Special ScienceTeacher I What is the sample space? tossing a die 𝑆 = 1,2,3,4,5,6
- 6. Statistics and Probability • PRINCESS P. DIPASUPIL • Special ScienceTeacher I What is the sample space? tossing two coins
- 7. Statistics and Probability • PRINCESS P. DIPASUPIL • Special ScienceTeacher I What is the sample space? Tossing a coin and a die
- 8. Statistics and Probability • PRINCESS P. DIPASUPIL • Special ScienceTeacher I Drawing a jack from standard deck of cards What is the SAMPLE SPACE? S={J♠, J♣, J⧫, J♥}
- 9. Statistics and Probability • PRINCESS P. DIPASUPIL • Special ScienceTeacher I What is the sample space? tossing a pair of dice S={ 11 21 31 41 51 61 12 22 32 42 52 62 13 23 33 43 53 63 14 24 34 44 54 64 15 25 35 45 55 65 16 26 36 46 56 66}
- 10. Statistics and Probability • PRINCESS P. DIPASUPIL • Special ScienceTeacher I What is the sample space? spinning this wheel
- 11. Statistics and Probability • PRINCESS P. DIPASUPIL • Special ScienceTeacher I What is the sample space? getting a sum of 7 when a pair of dice is tossed
- 12. Statistics and Probability • PRINCESS P. DIPASUPIL • Special ScienceTeacher I RANDOM VARIABLE a variable whose possible values are determined by chance
- 13. Statistics and Probability • PRINCESS P. DIPASUPIL • Special ScienceTeacher I typically represented by an uppercase letter, usually X, while its corresponding lowercase letter, x, is used to represent one of its values RANDOM VARIABLE
- 14. Statistics and Probability • PRINCESS P. DIPASUPIL • Special ScienceTeacher I X Random Variable x Value of a Random Variable RANDOM VARIABLE: Notations
- 15. Statistics and Probability • PRINCESS P. DIPASUPIL • Special ScienceTeacher I can only take a finite number of distinct values DISCRETE RANDOM VARIABLE countable
- 16. Statistics and Probability • PRINCESS P. DIPASUPIL • Special ScienceTeacher I can assume an infinite number of values in an interval between two specific values. CONTINUOUS RANDOM VARIABLE measurable
- 17. Statistics and Probability • PRINCESS P. DIPASUPIL • Special ScienceTeacher I measurable countable infinite finite nonnegative whole numbers fractions and decimals DISCRETE CONTINUOUS VS
- 18. Statistics and Probability • PRINCESS P. DIPASUPIL • Special ScienceTeacher I If the example illustrates a discrete random variable, type “D”. If the example illustrates a continuous random variable, type “C”. DISCRETE VS CONTINUOUS
- 19. Statistics and Probability • PRINCESS P. DIPASUPIL • Special ScienceTeacher I 5 4 the number of electric fans in your house 3 DISCRETE or CONTINUOUS 2 1
- 20. Statistics and Probability • PRINCESS P. DIPASUPIL • Special ScienceTeacher I amount of street food consumed by Nicholasians per day DISCRETE or CONTINUOUS 5 4 3 2 1
- 21. Statistics and Probability • PRINCESS P. DIPASUPIL • Special ScienceTeacher I the number of friends a person can have DISCRETE or CONTINUOUS 5 4 3 2 1
- 22. Statistics and Probability • PRINCESS P. DIPASUPIL • Special ScienceTeacher I the number of beautiful female students in SHS in San Nicholas III, Bacoor City, Cavite DISCRETE or CONTINUOUS 5 4 3 2 1
- 23. Statistics and Probability • PRINCESS P. DIPASUPIL • Special ScienceTeacher I the weight of all male students in this class DISCRETE or CONTINUOUS 5 4 3 2 1
- 24. Statistics and Probability • PRINCESS P. DIPASUPIL • Special ScienceTeacher I Determine whether the random variable X orY is discrete or continuous. 1. X = number of players in a randomly selected PBA team 2.Y = the height in inches of a randomly selected person inside the coffee shop 3. X = the number of things in your personal collection 4.Y = the number of COVID-19 tests done in a randomly selected day 5. X = the amount in pesos of fund allegedly stolen by former officials of a randomly selected government agency
- 25. Statistics and Probability • PRINCESS P. DIPASUPIL • Special ScienceTeacher I Determine whether the random variable X orY is discrete or continuous. 1. X = number of players in a randomly selected PBA team 2.Y = the height in inches of a randomly selected person inside the coffee shop 3. X = the number of things in your personal collection 4.Y = the number of COVID-19 tests done in a randomly selected day 5. X = the amount in pesos of fund allegedly stolen by former officials of a randomly selected government agency • discrete • continuous • discrete • discrete • continuous