Continuous Random Variable
1 hr 21 min 8 Examples
- Introduction to Video: Continuous Random Variables
- Overview and Properties of Continuous Probability Distributions
- Given the density function for a continuous random variable find the probability (Example #1)
- Determine x for the given probability (Example #2)
- Find the constant c for the continuous random variable (Example #3)
- Find the cumulative distribution function and use the cdf to find probability (Examples #4-5)
- For a continuous random variable find the probability and cumulative distribution (Example #6)
- Given the cumulative distribution function find the probability density function (Example #7)
- Graph the probability density function and verify f(x) is a pdf (Example #8a-b)
- Find the cumulative distribution function (Example #8c)
- Use the cumulative distribution function to find the probability (Example #8d)
Expected Value Variance Continuous Random Variable
1 hr 25 min 7 Examples
- Introduction to Video: Mean and Variance for Continuous Random Variables
- Properties and formulas for mean and variance of continuous random variables
- Find the mean and variance of a discrete random variable (Example #1)
- Find the mean and variance of a continuous random variable (Example #2)
- Determine the mean and variance of a continuous random variable (Example #3)
- Determine the mean of a discrete random variable (Example #4)
- Find the mean of the continuous random variable (Example #5)
- Given a triangular probability density function find the pdf formula (Example #6a)
- Using the pdf formula from part a, find the mean (Example #6b)
- Find the probability of the continuous distribution (Example #6c)
- Using various integration techniques, find the expected value and variance of the continuous random variable (Example #7)
Continuous Uniform Distribution
59 min 5 Examples
- Introduction to Video: Continuous Uniform Distribution
- Properties of a continuous uniform Distribution with Example #1
- Find the probability, mean, and standard deviation of a continuous uniform distribution (Examples #2-3)
- Find the mean and variance of a continuous uniform random variable (Example #4a)
- Determine the cumulative distribution function of the continuous uniform random variable (Example #4b)
- Find the probability of the continuous uniform distribution (Example #4c)
- Prove the formula for the mean of a continuous uniform distribution (Example #5a)
- Verify the formula for variance of a continuous uniform distribution (Example #5b)
Normal Approximation
47 min 5 Examples
- Introduction to Video: Normal Approximation of the Binomial and Poisson Distributions
- How to use the normal distribution to approximate the binomial or poisson with Example #1
- Use the normal distribution to approximate a poisson and binomial random variable (Examples #2-3)
- Find the probability of a binomial distribution using a normal approximation (Example #4)
- Find the probability of a Poisson distribution using a normal approximation (Example #5)
Exponential Distribution
1 hr 30 min 9 Examples
- Introduction to Video: Gamma and Exponential Distributions
- Overview of the Gamma Function and Gamma Distribution
- How to use the Gamma distribution properties and density function (Examples #1-2)
- Overview of the Erlang and Exponential Distribution and its properties
- Use integration of the exponential distribution density function to find probability (Example #3)
- Generate the exponential cumulative distribution function formulas
- Find the probabilities for the exponential distribution (Examples #4-5)
- Determine the probabilities for the exponential distribution (Example #6-7)
- Lack of Memory Principle for the Exponential Distribution with Examples #8-9
Weibull Lognormal Distribution
56 min 7 Examples
- Introduction to Video: Weibull and Lognormal Distributions
- Overview of the Weibull Distribution and formulas with Example #1
- Assume a Weibull distribution, find the probability and mean (Examples #2-3)
- Overview of the Lognormal Distribution and formulas
- Suppose a Lognormal distribution, find the probability (Examples #4-5)
- For a lognormal distribution find the mean, variance, and conditional probability (Examples #6-7)
Chapter Test
1 hr 28 min 15 Practice Problems
- Find the probability for the continuous distribution (Problem #1)
- Find the cumulative distribution function (Problem #2)
- Find the probability for the Normal distribution (Problem #3)
- What’s the probability a component lasts? (Problem #4)
- Find the probability for the Exponential distribution (Problem #5)
- Find the probability for the Lognormal distribution (Problem #6)
- Find the mean and probability for the Exponential distribution (Problem #7)
- What is the probability for the Gamma distribution (Problem #8)
- Find the probability for the continuous uniform distribution (Problem #9)
- Find the mean and variance for the continuous random variable (Problem #10)
- Find the probability for the Weibull distribution (Problem #11)
- Find the probability for the lognormal distribution (Problem #12)
- Find the probability using the normal distribution (Problem #13)
- What is the probability of the exponential distribution (Problem #14)
- Approximate the binomial distribution using the normal distribution (Problem #15)
