Statistical Distributions

"It is true that in quantum theory we cannot rely on strict causality. But by repeating the experiments many times, we can finally derive from the observations statistical distributions, and by repeating such series of experiments, we can arrive at objective statements concerning these distributions. "

Werner Heisenberg

Discrete random variable

What you have to know:

You must know how to calculate probabilities.
(If not, check this lesson)

Key Points

1. Watch the video:

2. Expected values problems. Watch this video
3. Fair games and expected value. Watch this video

Binomial distribution

What you have to know:

You must know how to calculate probabilities.
(If not, check this lesson)

Key Points

1. Watch the video:

Poisson distribution

What you have to know:

You must know how to calculate probabilities.
(If not, check this lesson)

Key Points

1. Watch the video:

Normal distribution

What you have to know:

You must know how to calculate probabilities.
(If not, check this lesson)

Key Points

1. Watch the video:

2. Example with Normal and Binomial distribution. Watch this video
3. Inverse Normal distribution exercise. Watch this video

Type I and Type II errors

What you have to know:

A probability of a type I error is the probability of rejecting H₀ when H₀ is true. For the normal distribution this will be equal to the significance level; for a discrete distribution this will be the probability of the statistic falling in the critical region.
In order to find the probability of a type II error, first find the critical region under the null hypothesis.
The probability of a type II error is the probability of the statistic not being in the critical region. This is calculated using a value for the parameter chosen from the alternative hypothesis.

Key Points

1. Watch the video:

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