up9_1280_wa-u4

.pdf

School

University of the People *

*We aren’t endorsed by this school

Course

1280

Subject

Statistics

Date

Nov 24, 2024

Type

pdf

Pages

6

Uploaded by ziadtsoubra

1 Written Assignment Unit 4 MATH 1280 Introduction to Statistics University of the People Jessica (Instructor) Nov 12, 2023
2 Given the table below, answer the following questions: Probability distributions are a fundamental concept in statistics. They describe the likelihood of different outcomes occurring in a random event. Probability tables are a useful way to represent probability distributions. They show the probability of each possible outcome of the event. Probability tables provide a quick, easy way to calculate the probability of different outcomes in a random event. They also help to identify outliers and patterns in the data, which can be useful for making decisions about future events (Illowsky et al., 2022). Completing the Missing Probability In the table provided, the missing probability is the probability of outcome 4. To complete the table, we need to make sure that the sum of all the probabilities is equal to 1. This is because the sum of the probabilities represents the total probability of the event occurring, which must be equal to 1. This can be done by multiplying each probability by 4. For example, the probability of outcome 1 is multiplied by 4, the probability of outcome 2 is multiplied by 4 and so on. After multiplying all the probabilities by 4, the total probability is equal to 1. (Illowsky et al., 2022). Therefore, the missing probability is: 1 - (0.12 + 0.18 + 0.30 + 0.15 + 0.10 + 0.05) = 0.20 Expected Value
3 The expected value of a probability distribution is the average of the possible outcomes, weighted by their probabilities. To calculate the expected value, we multiply each outcome by its probability and then sum the products: E(X) = Σ x * P(x) where: E(X) is the expected value x is an outcome P(x) is the probability of outcome x Using the table provided, we can calculate the expected value as follows: E(X) = (0 * 0.12) + (1 * 0.18) + (2 * 0.30) + (3 * 0.15) + (4 * 0.20) + (5 * 0.10) + (6 * 0.05) = 2.37 Therefore, the expected value of the probability distribution is 2.37. Standard Deviation The standard deviation of a probability distribution is a measure of how spread out the outcomes are. It is calculated by taking the square root of the variance, which is the average of the squared deviations from the mean: σ = √Var(X)
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help
Recommended textbooks for you
Text book image
College Algebra
Algebra
ISBN:9781337282291
Author:Ron Larson
Publisher:Cengage Learning
Text book image
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:Cengage Learning
Text book image
College Algebra
Algebra
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:Cengage Learning
Text book image
Holt Mcdougal Larson Pre-algebra: Student Edition...
Algebra
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
SEE MORE TEXTBOOKS
Recommended textbooks for you
Text book image
College Algebra
Algebra
ISBN:9781337282291
Author:Ron Larson
Publisher:Cengage Learning
Text book image
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:Cengage Learning
Text book image
College Algebra
Algebra
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:Cengage Learning
Text book image
Holt Mcdougal Larson Pre-algebra: Student Edition...
Algebra
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
SEE MORE TEXTBOOKS