# Statistical Analysis and Modeling in R: Working with Probability Distributions

R Programming 4.0+    |    Intermediate
• 12 videos | 1h 38m 24s
• Includes Assessment
Interpreting data is a core pre-processing step in data analysis and modeling. Use this course to practice using various dynamic statistical tools to explore and understand your data. During this course, you'll explore population distributions to model random variables, work with discrete and continuous probability distributions, and use discrete probability distribution types, such as the uniform, binomial, and Poisson distributions. You'll also examine continuous distributions, such as the normal and the exponential distributions. You'll round the course off by learning how to read and interpret QQ plots, which can be used to compare the distributions of two samples of data. When you're finished, you'll be able to use probability distributions to model events and understand your data.

## WHAT YOU WILL LEARN

• Discover the key concepts covered in this course Recall the sets of statistical tools used to understand data Compare and contrast population metrics with sample metrics Recall the characteristics of discrete and continuous probability distributions Sample and analyze data that follows uniform distribution Sample and analyze data which follows binomial distribution
• Calculate probabilities of events in the binomial distribution Sample and analyze data which follows uniform distribution Examine and interpret normal distributions and exponential distributions Interpret qq plots for normally and non-normally distributed data Use qq plots to compare samples from different distributions Summarize the key concepts covered in this course

## IN THIS COURSE

• In this video, you’ll learn more about the course and your instructor. In this course, you’ll explore statistical tools you can use to explore and understand your data. You’ll learn population distributions to model random variables and work with discrete and continuous probability distributions. You’ll learn the characteristic of discrete probability distributions such as the uniform distribution, the binomial distribution, and the Poisson distribution, as well as the normal distribution and the exponential distribution.
• In this video, you’ll learn more about statistics. Statistics is a mathematical body of science that pertains to the collection, analysis, interpretation, or explanation, and presentation of data. Statistics is about working with data, understanding your data, exploring your data, and interpreting results from your data. Statistics is concerned with the use of data in the context of uncertainty and decision making in the face of uncertainty.
• 3.  Population and Sample Metric Comparisons
In this video, you’ll learn more about the terms population and sample. The term population refers to all the data that exists in the universe. It's impossible to work with data for the entire population. When you have data to work with, that data will be a sample. A sample represents a subset of the population. This subset is representative of the population as a whole.
• 4.  Characteristics of Probability Distribution Types
In this video, you’ll learn more about probability distributions. Probability distribution is a mathematical function that shows the possible values for a variable and how often those values occur. The variable refers to your data. Your variables have their own range of values, and different values occur with different frequencies or different probabilities of occurrence. A probability distribution is a mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment.
• 5.  Sampling and Analyzing Uniform Distribution Data
In this video, you’ll learn more about RStudio to write R code. You’ll see RStudio is a freely available integrated development environment or IDE for R. RStudio includes a console, a syntax-highlighting editor that supports direct code execution. RStudio also has tools for plotting history, debugging, workspace management, and so on. You’ll discover RStudio Desktop is freely available for anyone to download and use. You’ll need to download RStudio on your computer.
• 6.  Sampling and Analyzing Binomial Distribution Data
In this video, you’ll learn more about probability distributions. You’ll learn another discrete probability distribution, the binomial distribution. The binomial distribution summarizes the probability that the outcome will be one of two independent values. You’ll learn a variable that is binomially distributed can have only two possible outcomes, heads or tails, true or false, here or there. These two outcomes must be independent. One outcome should not be more possible because of the previous outcome.
• 7.  Computing Probabilities in Binomial Distributions
In this video, you’ll learn more about computing probabilities in binomial distributions. You’ll remember the rbinom function from the earlier video gives you data points generated from a binomial distribution with certain parameters. The dbinom function in R also works with binomial distributions. This is the function that gives you the density. You’ll look at an example here.
• 8.  Sampling and Analyzing Poisson Distribution Data
In this video, you’ll learn more about the Poisson distribution. The Poisson distribution is also a discrete probability distribution. You’ll learn the Poisson distribution is commonly used to model the number of expected events for a process, as long as you know the average rate at which events occur during a unit of time. Onscreen, you’ll see to generate data points from a Poisson distribution using a specific example.
• 9.  Examining Normal and Exponential Distributions
In this video, you’ll learn more about the normal distribution, a continuous probability distribution. The normal distribution is a continuous probability distribution that’s symmetric around the mean or the average of your data. The probability density curve of a normal distribution is known as a bell curve because it's shaped like a bell. In a normal distribution, data values that are close to the mean occur more often than values far away from the mean.
• 10.  Interpreting QQ Plots Using R
In this video, you’ll learn more about QQ plots. QQ Plots are used to assess whether the data you're working with plausibly came from some theoretical distribution. In statistical analysis, you might assume your data is drawn from a population that is normally distributed. This is a requirement for your statistical test. An easy way to test whether this data was from a normal distribution is to use QQ plots.
• 11.  Using QQ Plots in R to Compare Datasets
In this video, you’ll work with QQ norm and non-normally distributed data. You'll use QQ norm to get a visual check on whether your data points are normally distributed. First, you’ll use the rexp or rexp function to generate data points drawn from an exponential distribution. You’ll generate a total of 1000 data points. The rate for this exponential distribution is 0.35. Because it’s artificially generated data, you know the data is exponentially distributed.
• 12.  Course Summary
In this video, you’ll summarize what you’ve learned in this course. You’ve explored the statistical tools that analysts use to understand and interpret their data. You covered descriptive statistics used to summarize data and inferential statistics which are used to make deductions from a sample about the population the sample represents. You also learned about probability distributions and how they help you understand data. You explored discrete probability distributions which are used with categorical data.

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