What you'll learn
Learn how to use R to solve a wide variety of probability problems
Learn about important probability functions like the PMF, PDF, CDF, Inverse CDF, and how to use them to solve problems.
Master important probability distributions including Bernoulli, Binomial, Normal, Geometric, Hypergeometric, Exponential, Poisson, Negative Binomial, and Gamma
Learn how to simulate data to answer questions about probability distributions.

Requirements
Strong skills in basic algebra and arithmetic
No knowledge of R is assumed, some experience with coding would be helpful
No prior knowledge of probability is assumed

Description
This course offers an in-depth exploration of probability, shedding light on various statistical distributions using R's r/d/p/q functions.The course includes:5 hours of video lectures30 coding exercises with over 100 problems, including detailed hints and step-by-step solutions, offering hands-on experience with RYou will learn about:Discrete Distributions including the Bernoulli, Binomial, Hypergeometric, Geometric, Negative Binomial and Poisson distributionsThe Normal distribution and the Central Limit TheoremOther continuous distributions including the Exponential, Gamma, Poisson, and Uniform distributions.Hands-on examples using R's r/d/p/q functions: generating random numbers, computing probabilities, medians, quantiles, and more.Contextual understanding and application of probability mass functions (PMFs), probability density functions (PDFs), cumulative distribution functions (CDFs) , and inverse cumulative distribution functions (inverse CDFs/quantile functions)The expected value and standard deviation of the probability distributions, and how to use these in applications involving the central limit theorem.This course is perfect for:Individuals aiming for a strong foundation in probability and the various probabilities distributions used in statistics and data science.Current and aspiring data analysts and data scientists who wish to harness the potential of R for simplifying probability calculations.Anybody who uses R and wants to use R to learn probability quickly, using an innovative computer-centric approach.

Overview
Section 1: Introduction

Lecture 1 Introduction

Lecture 2 R Basics

Section 2: Bernoulli Random Variables

Lecture 3 Binary Random Variables, Sample Space

Lecture 4 Simulating Bernoulli random variables with rbinom()

Lecture 5 Parameters - The population proportion

Lecture 6 Sample statistics - mean() for calculating sample proportions

Lecture 7 dbinom()

Section 3: Binomial Random Variables

Lecture 8 Binomial random variables

Lecture 9 mean(rbinom()), Law of Large Numbers

Lecture 10 Estimating probabilities with mean() and rbinom()

Lecture 11 dbinom() intro

Lecture 12 Expected Value

Lecture 13 Variance and Standard Deviation

Lecture 14 cdf and pbinom()

Lecture 15 Other types of inequalities and intervals

Lecture 16 Visualizing the cdf

Lecture 17 The median

Lecture 18 qbinom()

Lecture 19 Problem-solving with qbinom()

Section 4: Hypergeometric Random Variables

Lecture 20 Hypergeometric random variables

Section 5: Normal Random Variables

Lecture 21 Normal Random Variables and the empirical rule

Lecture 22 Empirical rule with rnorm()

Lecture 23 dnorm() and probability density functions (pdfs)

Lecture 24 pnorm()

Lecture 25 qnorm()

Section 6: Sums, CLT, Normal Approximations

Lecture 26 Expected value of sum

Lecture 27 Variance and standard deviation of sum

Lecture 28 The sum of normal random variables is a normal random variable

Lecture 29 Central Limit Theorem: Normal Approximation to the Binomial Distribution

Section 7: Geometric Random Variables

Lecture 30 Geometric Random Variables

Lecture 31 rgeom()

Lecture 32 dgeom() and the pmf of geometric random variables

Lecture 33 Expected Value and Standard Deviation

Lecture 34 CDFs and pgeom()

Lecture 35 Inverse cdf, quantiles, qgeom()

Section 8: Negative Binomial Random Variables

Lecture 36 Negative Binomial Random Variables

Lecture 37 rnbinom()

Lecture 38 dnbinom()

Lecture 39 Mean and standard deviation

Lecture 40 pnbinom()

Lecture 41 qnbinom()

Lecture 42 Normal Approximations to the negative binomial

Section 9: Exponential Random Variables

Lecture 43 Exponential Random Variables

Lecture 44 rexp()

Lecture 45 dexp()

Lecture 46 Expected value and standard deviation

Lecture 47 pexp() and memorylessness

Lecture 48 qexp()

Section 10: Gamma Random Variables

Lecture 49 Gamma Random Variables and rgamma()

Lecture 50 Expected Value and Standard Deviation

Lecture 51 dgamma() and pgamma()

Lecture 52 qgamma()

Lecture 53 Normal approximation to the gamma distribution

Section 11: Poisson Random Variables

Lecture 54 Poisson Random Variables and rpois()

Lecture 55 dpois()

Lecture 56 Mean and Standard Deviation

Lecture 57 ppois()

Lecture 58 qpois()

Lecture 59 Different time periods, Sums of Poisson Random Variables

Lecture 60 Normal Approximation

Section 12: Uniform Random Variables

Lecture 61 Uniform Random Variables, dunif()

Lecture 62 Mean and standard deviation

Lecture 63 punif()

Lecture 64 qunif() and the inverse transform method

Current and aspiring data scientists and data analysts,Anyone learning R and wanting to master important probability functions,Anybody wanting to learn probability in an innovative way through programming and R

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