discrete random variables and continuous random variables
- 3. Sample Space List the sample space of the following experiments. 1. Tossing two coins 2. Rolling a die and tossing a coin at the same time. 3. Getting a red ball when two balls are randomly picked from a box containing 5 red balls and 6 blue balls.
- 4. Random Variable A random variable is a function that associates a real number to each element in the sample space. It is a variable whose values are determined by chance.
- 5. Suppose you are to test three random eggplants from a harvest to see if there are worms in it. You want to find out the number of eggplants attacked by worms. Use W to represent if there is a worm attack in an eggplant and N if there is none. Let Z be the random variable representing the number of eggplants attacked by worms. Find the values of the Let’s try!
- 6. Three coins are tossed. Let X be the random variable representing the number of heads occur. Find the values of the random variable X. Practice!
- 7. 1. A dog gave birth to a litter of six puppies. Three of them are male while the rest are female. If you are to be given three of these puppies at random, list all the elements of the sample space using the letters M and F for male puppies and female puppies, respectively. Then assign a value to the random variable X representing the number of male puppies you receive. Activity #1!
- 8. 2. A pair of dice is rolled. Let X be the random variable representing the number of getting even numbers. Find the values of the random variable X. Activity #1!
- 9. A random variable is a discrete random variable if its set of possible outcomes is countable. A random variable is a continuous random variable if it takes on values on a continuous scale.
- 10. Discrete Random Variable • the number of vowels in the English alphabet • the number of honor students in a class • the number of satellites orbiting the Earth • count of words encoded per minute • yearly death due to cancer Examples:
- 11. Continuous Random Variable • amount of sugar in a cup of coffee • time needed to solve a Rubik’s cube • volume of diesel used in a trip • length of a cellphone charger • distance between two barangays Examples:
- 12. • the blood pressures of a group of students the day before the final exam • the height of a player on a basketball team • the number of coolers sold in a cafeteria during lunch • the temperature in degrees Celsius on February 5th in Masinloc, Zambales • the number of goals scored in a soccer game Let’s try!
- 13. • the speed of a car • the distance a golf ball travels after being hit • the weight of a rhinoceros • the number of female STEM students • the number of deaths per year attributed to lung cancer • the amount of paint utilized in a building project • the number of new teachers in SASMA Let’s try!
- 14. • the number of defective computers produced by a manufacturer • the weight of newborns each year in a hospital • the number of diamond suits in a deck of cards • the number of dropouts from SASMA in ten years • the number of Andreans with Android phones • the time needed to finish the test • the number of Olympic gold medalists Let’s try!
- 15. • the number of broken chairs in Kinder Garten • the number of Math club members • the weight of 10,000 people • the number of children in a family • the number of defective bulbs in a box of 10 • the amount of rain in a day • the length of hairs on a horse Let’s try!
- 16. Event (E) Probability (P) Getting a prime number in a single roll of die 𝟏 𝟐 Getting a red queen when a card is drawn from a deck 𝟏 𝟐𝟔 Getting a numbered card when a card is drawn from the pack of 52 cards 𝟗 𝟏𝟑 Getting a sum of 7 when two dice are thrown 𝟏 𝟔
- 17. Probability Distribution or Probability Mass Function A discrete probability distribution or a probability mass function consists of the values a random variable can assume and the corresponding probabilities of the values.
- 18. Determine whether the distribution represents a probability distribution. Explain your answer. Practice! X 1 5 8 7 9 P(X) 𝟏 𝟑 𝟏 𝟑 𝟏 𝟑 𝟏 𝟑 𝟏 𝟑
- 19. Determine whether the distribution represents a probability distribution. Explain your answer. Practice! X 0 2 4 6 8 P(X) 𝟏 𝟔 𝟏 𝟔 𝟏 𝟑 𝟏 𝟔 𝟏 𝟔
- 20. Determine whether the given values can serve as the values of a probability distribution of the random variable X that can take on only the values 1, 2 and 3. Explain your answer. 1. P(1) = 0.08, P(2) = 0.12, P(3) = 1.03 2. P(1) = 9 14 , P(2) = 4 14 , P(3) = 1 14 Practice!
- 21. Suppose three cellphones are tested at random. Let D represent the defective cellphone and N represent the non-defective cellphone. Also, let Y be the random variable representing the number of defective cellphones. Find the values of the random variable Y. Practice!