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Understanding Random Variables and Probability Distributions, Summaries of Mathematics

An introduction to random variables, their types (discrete and continuous), and the computation of probabilities associated with them. It also covers the properties of discrete probability distributions and includes exercises to practice identifying discrete and continuous random variables, as well as finding their probabilities and properties.

Typology: Summaries

2022/2023

Uploaded on 03/16/2024

cristine-mae-ramos
cristine-mae-ramos 🇵🇭

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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. "anong mahirap dyan e letters lang naman yan" yung letters: | mihi +— | | — re —} aura gees ea |e wi | 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?