Chapter 3: Change

[entropidelic]

change

An important feature of probability is how related it is to real world problems. The most fruitful probabilities fields are the ones that approach this kind of problem. You can see them being used in almost every scientific discipline.

I don't think the statement of probability fields is quite correct. Specifically,

The most fruitful probabilities fields are the ones that approach this kind of problem.

maybe add a cite or delete this line

[entropidelic]

add

As an exercise, try to figure out why each of these events are linked to each subset.

right after this part:

A = “The red wall was not taken” = ${(G,B)(G,W)(B,W)}$ B = “The green and the blue ball were taken” = ${(G,B)}$

[entropidelic]

When talking about the probability of the entire sample space, my suggestion was

You can think of this as the probability that something will happen. As a quick example, consider throwing a coin. The sample space will consist of Heads and Tails. The probability of the sample space is indeed $1$, because we are sure one of these two outcomes will be obtained.

and @pefontana suggestion was

Since we define the sample space as the aggregate of all the possible outcomes of an experiment, we can deduce that the probability of the entire sample space $S$ is unity, or $P{S} = 1$. You can think of this as the probability that something will happen. As a quick example, consider throwing a coin. The sample space will consist of “head” and “tail”, the probability of the sample space is indeed $1$, because we are sure one of these two outcomes will be obtained. One last thing to mention is that probability, being a measure of our own belief or certainty in the occurrence of an event, does not determine whether the event occurs or not. For this reason, events may still occur when we assign them probability $0$, and they might not occur if we assign them probability $1$. When a coin is tossed, it does not necessarily fall heads or tails; it can roll away or stand on its edge. Nevertheless, we shall agree to regard "head" and "tail" as the only possible outcomes of the experiment. This convention simplifies the theory without affecting its applicability.

[entropidelic]

when talking about independent events, the part

$P(R|L) = P(R) \text{ either } P(L|R) = P(L)$

is a bit confusing. I don't understand why "either" was used here

[entropidelic]

an explanation of logical operators ('and', 'or', etc) and their relationship with sets should be nice for consistency in the chapter

[entropidelic]

typo when explaining Poisson distribution parameter lambda

[entropidelic]

When we work with continuous variables it is pointless to talk about the probability of a single x value.

I would change to

it is pointless to talk about the probability of a particular and unique value of x

in:

Think of it in a mathematical way, in a number line there are infinity points in between 0 and 0,01.

change "infinity" to "infinite". Also some arrangements at the end of the sentence:

in between, for example, $0$ and $0.01$, as would happen in any real-number interval.

in:

In this case, our continuous variable is women's height, since there are infinitely possible heights it has no sense to talk about the probability of a single height, like $P(6 in)$.

"it has no sense" is not quite correct, use "it makes no sense"

in:

Probability in the continuous case is always computed in an interval.

add, at the end:

an interval, although this interval can be as small as we like.

in:

For example, suppose we want to know the probability that a randomly selected woman measures between 60 and 65 inches.

"measures" is not quite correct. Use

suppose we want to know the probability that a randomly selected woman's height is between 60 and 65 inches.

in:

To know it we need to calculate the area under the density curve in the intervals x = [60,65].

suggestion

To compute it, we need to calculate the area under the density curve in the interval [60, 65].