Discrete Random Variable
1 hr 14 min 14 Examples
- Introduction to Video: Discrete Random Variables
- Overview of Discrete Random Variables, Continuous Random Variables, and Discrete Probability Distributions
- Find the probability distribution if a coin is tossed three times (Example #1)
- Determine if the given table is a probability distribution (Examples #2-4)
- Given the probability distribution find the probability of an event and create a histogram (Examples #5-8)
- Given the probability mass function find the probability of an event (Example #9)
- Construct a probability distribution for a carnival game (Example #10)
- Construct a tree diagram and probability distribution for defective batteries (Example #11)
- Overview of Cumulative Distribution Functions with Example #12
- Find the cumulative function and obtain its graph (Example #13)
- Determine the probability function given the cumulative function (Example #14)
Standard Deviation Variance Expected Value
43 min 5 Examples
- Introduction to Video: Mean and Variance of a Discrete Random Variable
- How to find the expected value, variance and standard deviation of a discrete random variable with Example #1
- Given the probability distribution of X find the mean and variance (Example #2)
- Given the probability distribution and the mean, find the value of c in the range of X (Example #3)
- What is the expected profit and variability? (Example #4)
- How do rental vs owned housing units compare? Make a histogram comparing probability distributions (Example #5a)
- How do rental vs owned housing units compare? Find the mean number or expected number of rooms for both types of housing units (Example #5b)
- How do rental vs owned housing units compare? Find the standard deviation for both owner-occupied and renter-occupied distributions (Example #5c)
Transformation of Random Variables
49 min 4 Examples
- Introduction to Video: Transforming and Combining Discrete Random Variables
- Overview of how to transform random variables and combine two random variables to find mean and variance
- Find the new mean and variance (Example #1)
- Find the new mean and variance given two discrete random variables (Example #2)
- Find the mean and variance of the probability distribution (Example #3)
- Find the mean and standard deviation of the probability distribution (Example #4a)
- Find the new mean and standard deviation after the transformation and graph the distribution (Example #4b)
- Find the mean and standard deviation of the linear transformation (Example #4c)
Discrete Uniform Distribution
21 min 6 Examples
- Introduction to Video: Discrete Uniform Distributions
- How to create, identify and graph a discrete uniform distribution? (Examples #1-2)
- Formulas for finding the mean and variance of a discrete uniform distribution (Example #3)
- Write the discrete uniform distribution and find the mean and variance (Example #4)
- Find the mean and variance given the range of a discrete uniform random variable (Example #5)
- Find the expected value and variance of X for a discrete uniform random variable (Example #6a)
- Determine the mean and variance after the transformation of the discrete uniform random variable (Example #6b)
Binomial Distribution
1 hr 12 min 11 Examples
- Introduction to Video: Bernoulli and Binomial Random Variables
- Bernoulli Random Variable Overview with Examples #1-2
- Binomial Random Variable and Distribution Overview
- Determine if the random variable represents a binomial distribution (Examples #3-6)
- Find the probability, expected value, and variance for the binomial distribution (Examples #7-8)
- Find the probability and cumulative probability, expected value, and variance for the binomial distribution (Examples #9-10)
- Find the cumulative probability, expected value, and variance for the binomial distribution (Example #11)
Geometric Distribution
44 min 6 Examples
- Introduction to Video: Geometric Distribution
- Overview of Geometric Random Variable with Examples #1-3
- Find the probability, expected value and variance for the geometric distribution involving the success of starting a lawnmower(Example #4)
- Find the probability and expectation for the distribution of rolling two dice (Example #5)
- Find the probability, expected value, and variance for passing a placement test (Example #6)
- Overview of Lack of Memory principle for geometric distributions
Negative Binomial Distribution
56 min 7 Examples
- Introduction to Video: Negative Binomial Distribution
- What is the Negative Binomial Distribution and its properties?
- Given a negative binomial distribution find the probability, expectation, and variance (Example #1)
- Find the probability of winning 4 times in X number of games (Example #2)
- Find the probability for the negative binomial distribution (Examples #3-4)
- Find the probability of failure for the the negative binomial distribution (Example #5)
- Find mean, standard deviation and probability for the distribution (Example #6)
- Find the probability using the negative binomial distribution and the binomial distribution (Example #7)
Hypergeometric Distribution
51 min 6 Examples
- Introduction to Video: Hypergeometric Distribution
- Overview of the Hypergeometric Distribution and formulas
- Determine the probability, expectation and variance for the sample (Examples #1-2)
- Find the probability and expected value for the sample (Examples #3-4)
- Find the cumulative probability for the hypergeometric distribution (Example #5)
- Overview of Multivariate Hypergeometric Distribution with Example #6
Poisson Distribution
52 min 6 Examples
- Introduction to Video: Poisson Distribution
- Overview of the Poisson Distribution and it’s properties
- Given a Poisson distribution find the probability, expectation and standard deviation (Examples #1-2)
- Find the probability and cumulative probability given a Poisson Distribution (Examples #3-4)
- Find the expected cost using definition of expectation for a poisson distribution (Example #5)
- Verify the expected value of a Poisson distribution using Taylor series (Example #6)
Chapter Test
1 hr 40 min 15 Practice Problems
- Pain scale follows a discrete probability distribution find mean and probability (Problem #1)
- Complete the transformation and find the new mean and variance (Problem #2)
- Find the probability for the Binomial Distribution (Problem #3)
- Find the probability using the Poisson, Binomial and Geometric Distributions (Problem #4)
- Find the probability using the Multivariate Hypergeometric Distribution (Problem #5)
- Find the probability using the Poisson Distribution (Problem #6)
- Find the probability for the Negative Binomial Distribution (Problem #7)
- Find the probability for the Hypergeometric Distribution (Problem #8)
- Find the probability and mean for the Geometric Distribution (Problem #9)
- Find the probability and expected failures for the Binomial Distribution (Problem #10)
- Find the probability, mean and variance for the Hypergeometric Distribution (Problem #11)
- Use the Binomial random variable to create a probability distribution, histogram and find the probability (Problem #12)
- Find the probability using the Hypergeometric Distribution (Problem #13)
- Find the probability using the Negative Binomial Distribution (Problem #14)
- Find the probability using the Poisson and Binomial Distributions (Problem #15)