Download Understanding Random Variables and Probability Distributions and more Summaries Mathematics in PDF only on Docsity! RANDOM VARIABLE Statistics and Probability Week 1 learning competencies At the end of this session, the students are able to: 1. illustrate a random variable; 2. distinguish between a discrete and a continuous random variable; 3. find the possible value of a random variable; RANDOM VARIABLE CONTINUOUS random variable It has infinitely many values, and the collection of values is not countable (Triola, 2018) DISCRETE random variable It is a collection of values that is finite or countable (Triola, 2018) EXERCISE 1 1. P: The number of defective computers produced by a manufacturer. 2. Q: The weight of newborns each year in a hospital. 3. R: An amount of paint utilized in a building project. 4. S: The number of dropouts in a school district for a period of 10 years. 5. T: The number of female athletes. Instruction: Determine if the given statement is discrete or continuous. RANDOM VARIABLE 6. U: The time needed to finish the test. 7. V: The amount of sugar in a cup of coffee. 8. W: The number of accidents per year at an intersection. 9. X: The average amount of electricity consumed per household per month. 10. Y: The number of deaths per year attributed to lung cancer. Instruction: Determine if the given statement is discrete or continuous. EXAMPLE 2 Three coins are tossed. Let "Z" be the random variable representing the number of heads that occurs. Find the values of the random variable "Z" with its corresponding probabilities.
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PROPERTIES DISCRETE P.D. If X is a random variable with x elements, then a. The probability of each value is between 0 and 1, inclusive. b. The sum of all probabilities is 1. EXERCISE 2 Instruction: Determine whether the given table is probability distribution or not. EXERCISE 3 The table below is a probability distribution of a discrete random variable X. Find the following probabilities. LeARN MORE How many ways you can choose 2 pens? LeARN MORE How many ways you can choose 2 pens? LeARN MORE How many ways you can choose 3 pens? Let's get deeper How many ways we can select 3 students from 5? 1. How many ways we can select 4 students from 6? 2. Let's get deeper Suppose we have 5 boys and 4 girls. How many ways we can select 3 boys and 2 girls? Let's get deeper Suppose we have 5 boys and 4 girls. How many ways we can select 3 boys and 2 girls? (5C3)(4C2)=60 Let's get deeper Suppose we have 2 defective and 3 nondefective items and we can only select three. How many ways you can select 1 defective item? Let's get deeper Suppose we have 2 defective and 3 nondefective items and we can only select three. How many ways you can select 1 defective item? (2C1)(3C2)=6 Let's get deeper Suppose we have 2 defective and 3 nondefective items and we can only select three. How many ways you can select 2 defective items? Let's DIVE DEEPER Suppose we have 2 defective and 3 nondefective items and we can only select three. What is the probability of getting 0 defective items? Let's DIVE DEEPER Suppose we have 2 defective and 3 nondefective items and we can only select three. What is the probability of getting 1 defective items? Let's DIVE DEEPER Suppose we have 2 defective and 3 nondefective items and we can only select three. What is the probability of getting 1 defective items?