# Secondary Catalogue

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- Discrete Random Variables

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## Series: Discrete Random Variables

### Bernoulli Random Variables

A Bernoulli random variable is a special category of binomial random variables. Specifically, with a Bernoulli random variable, we have exactly one trial only (binomial random variables can have multiple trials), and we define “success” as a...Show More

A Bernoulli random variable is a special category of binomial random variables. Specifically, with a Bernoulli random variable, we have exactly one trial only (binomial random variables can have multiple trials), and we define “success” as a 1 and “failure” as a 0. Show Less

### Binomial Random Variables

Remember that “bi” means two, so a binomial variable is a variable that can take on exactly two values. A coin is the most obvious example of a binomial variable because flipping a coin can only result in two values: heads or tails.

### Combinations of Random Variables

The combination of two random variables is the sum or difference of two variables. For instance, if I keep track of the time I spend walking each day, and separately keep track of the time I spend cycling each day, then I have two separate random...Show More

The combination of two random variables is the sum or difference of two variables. For instance, if I keep track of the time I spend walking each day, and separately keep track of the time I spend cycling each day, then I have two separate random variables. But if I want to combine these two, then I can add the variables. In this video we'll look at what happens to the mean, variance, and standard deviation of the combination, based on what we know about the means, variances, and standard deviations of the individual random variables. Show Less

### Discrete Probability

A discrete random variable is a variable that can only take on discrete values. For example, if we flip a coin twice, we can only get heads zero times, one time, or two times. We can’t get heads 1.5 times, or 0.31 times. In this video we'll...Show More

A discrete random variable is a variable that can only take on discrete values. For example, if we flip a coin twice, we can only get heads zero times, one time, or two times. We can’t get heads 1.5 times, or 0.31 times. In this video we'll look at how to calculate probability for discrete variables like this. Show Less

### Geometric Random Variables

The difference is that for a geometric random variable, we’re looking at how many trials we have to use until we get a certain success. For a binomial random variable, we decided ahead of time on a certain number of trials. But for a geometric...Show More

The difference is that for a geometric random variable, we’re looking at how many trials we have to use until we get a certain success. For a binomial random variable, we decided ahead of time on a certain number of trials. But for a geometric random variable, we’ll run an infinite number of trials until we get a success. Most of the conditions we put on the binomial random variable still apply to the geometric random variable: each trial must be independent, each trial can be called a "success" or "failure," and the probability of success on each trial is constant. Show Less

### Permutations and Combinations

In order to answer many probability questions, we need to understand permutations and combinations. A permutation is the number of ways we can arrange a set of things, and the order matters. On the other hand, a combination is the number of ways...Show More

In order to answer many probability questions, we need to understand permutations and combinations. A permutation is the number of ways we can arrange a set of things, and the order matters. On the other hand, a combination is the number of ways we can arrange a set of things, but the order doesn’t matter. Show Less

### Poisson Distributions

A Poisson process calculates the number of times an event occurs in a period of time, or in a particular area, or over some distance, or within any other kind of measurement, and the process has particular characteristics. In this video we'll...Show More

A Poisson process calculates the number of times an event occurs in a period of time, or in a particular area, or over some distance, or within any other kind of measurement, and the process has particular characteristics. In this video we'll look at how to use a Poisson process to model a discrete random variable. Show Less

### Transforming Random Variables

In this video we'll look at how to transform a random variable by shifting or scaling it. Shifting a data set means that we add or subtract the same value from every point in the data set. Scaling a data set means that we multiply every point in...Show More

In this video we'll look at how to transform a random variable by shifting or scaling it. Shifting a data set means that we add or subtract the same value from every point in the data set. Scaling a data set means that we multiply every point in the data set by the same value. When we shift the data set, the mean, median, and mode all shift by the same amount, but the range, IQR, and standard deviation remain the same. And when we scale a data set, the mean, median, mode, range, IQR, and standard deviation all scale by the same amount. Show Less

### “At Least” and “At Most,” and Mean, Variance, and Standard Deviation

For any binomial random variable, we can calculate the probability of at least some number of events occurring, or the probability of at most some number of events occurring. For instance, the probability of pulling at least 3 red marbles when we...Show More

For any binomial random variable, we can calculate the probability of at least some number of events occurring, or the probability of at most some number of events occurring. For instance, the probability of pulling at least 3 red marbles when we pull 5 marbles from a bag (this would mean pulling 3, or 4, or 5 red marbles), or the probability of pulling at most 3 red marbles when we pull 5 marbles from a bag (this would mean pulling 0, or 1, or 2, or 3 red marbles). Show Less