Intro to binomial distributions (better name here)

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Learning objectives

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Teaching opportunities and challenges

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Class design

Warm-up

An exercise on evaluating probabilities here (simple ones, I can use others with conditional probability later on)

X: number of heads after 10 flips of my coin

Binomial variable:

Each trial can be classified as either a success or failure (and these names are subjective, you may select whatever you prefer to classify as a success)
Fixed (finite) number of trials (the result of the previous one does not affect the next trial). In our case, the probability of getting heads in a flip does not influence the next flip.
Probability of success in each trial is constant (trials are independent and the probability of success does not change with "time")

Examples of what would be and what would not be binomial variables

Use this app to serve as an inspiration to do mine, where the graph changes with the success rate

That other app to evaluate binomial distributions (there is also that yellow page that I can steal)

Interesting: this video

Continuous random variables: (define here)

Let's define the continuous random variable $X$ as being the number of tails when tossing a fair coin four times.

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What is the meaning of

P(X=0)

? Does it make sense, to evaluate

P(X=5)

in this context? Explain with rich detail.