Any answer will be a matter of opinion, but I have taught lots of courses using what I believe to be a fairly standard order of presentation. I think there are good reasons for it and will discuss some of them.

Many elementary probability courses start with empirical discrete distributions. Proportions of various colors of candy bits in a large package of M&M's Skittles, or whatever. Some combinatorial material provides a basis for a few elementary distributions. Some basic rules of of probability are discussed.

After that and a discussion of tossing fair coins it is natural to get into a discussion of binomial distributions, which can involve some of the combinatorial arguments and probability rules. Also, a proof or discussion of the Law of Large numbers often appears at this point.

Next, depending on the level and applied nature of the course, it may be natural to discuss Poisson distributions as a limiting case of binomial one, and geometric and negative binomial distributions as waiting times for events already discussed in a binomial context. and to consider hypergeometric distributions as a generalization of binomial distributions where trials are not independent.

At some point a bridge needs to be crossed to discuss how continuous distributions differ fundamentally from discrete ones. Often starting with a brief mention of uniform distributions because of their mathematical simplicity, it is customary to spend a lot of time on normal distributions, because of their widespread use in applications, and because the Central Limit Theorem shows (or illustrates) convergence to normal.

Then a discussion of using normal distributions to approximate binomial probabilities seems mandatory. (At this point it seem especially worthwhile to show how better results are available from statistical software.)

Next, some courses introduce exponential distributions, which are widely used in applications and are in many respects simpler to handle than normal distributions. That can lead to a discussion of other gamma family distributions. If the course has any kind of Bayesian flavor, beta distributions are often discussed as natural prior distributions for binomial success probabilities.

The specific distributions discussed later in the course depend on the purpose of the course in a theoretical or applied program. It is not possible in a single course to deal with all of the distributions and relationships among them that are displayed on your link. From there on there seems to be no traditional order as various objectives are pursued.

Any answer will be a matter of opinion, but I have taught lots of courses using what I believe to be a fairly standard order of presentation. I think there are good reasons for it and will discuss some of them.

Many elementary probability courses start with empirical discrete distributions. Proportions of various colors of candy bits in a large package of M&M's Skittles, or whatever. Some combinatorial material provides a basis for a few elementary distributions. Some basic rules of of probability are discussed.

After that and a discussion of tossing fair coins it is natural to get into a discussion of binomial distributions, which can involve some of the combinatorial arguments and probability rules. Also, a proof or discussion of the Law of Large numbers often appears at this point.

Next, depending on the level and applied nature of the course, it may be natural to discuss Poisson distributions as a limiting case of binomial one, and geometric and negative binomial distributions as waiting times for events already discussed in a binomial context. and to consider hypergeometric distributions as a generalization of binomial distributions where trials are not independent.

At some point a bridge needs to be crossed to discuss how continuous distributions differ fundamentally from discrete ones. Often starting with a brief mention of uniform distributions because of their mathematical simplicity, it is customary to spend a lot of time on normal distributions, because of their widespread use in applications, and because the Central Limit Theorem shows (or illustrates) convergence to normal.

Then a discussion of using normal distributions to approximate binomial probabilities seems mandatory. (At this point it seems especially worthwhile nowadays to show how better results are available from statistical software.)

Next, some courses introduce exponential distributions, which are widely used in applications and are in many respects simpler to handle than normal distributions. That can lead to a discussion of other gamma family distributions. If the course has any kind of Bayesian flavor, beta distributions are often discussed as natural prior distributions for binomial success probabilities.

The specific distributions discussed later in the course depend on the purpose of the course in a theoretical or applied program. It is not possible in a single course to deal with all of the distributions and relationships among them that are displayed on your link. From there on there seems to be no traditional order as various objectives are pursued.

Any answer will be a matter of opinion, but I have taught lots of courses using what I believe a fairly standard order of presentation. I think there are good reasons for it and will discuss some of them.

Many elementary probability courses start with empirical discrete distributions. Proportions of various colors of candy bits in a large package of M&M's Skittles, or whatever. Some combinatorial material provides a basis for a few elementary distributions. Some basic rules of of probability are discussed.

After that and a discussion of tossing fair coins it is natural to get into a discussion of binomial distributions, which can involve some of the combinatorial arguments and probability rules. Also, a proof or discussion of the Law of Large numbers often appears at this point.

Next, depending on the level and applied nature of the course, it may be natural to discuss Poisson distributions as a limiting case of binomial one, and geometric and negative binomial distributions as waiting times for events already discussed in a binomial context. and to consider hypergeometric distributions as a generalization of binomial distributions where trials are not independent.

At some point a bridge needs to be crossed to discuss hoe continuous distributions differ fundamentally from discrete ones. Often starting with a brief mention of uniform distributions because of their mathematical simplicity, it is customary to spend a lot of time on normal distributions, because of its widespread use in applications, and because the Central Limit Theorem shows (or illustrates) convergence to normal.

Then a discussion of using normal distributions to approximate binomial probabilities seems mandatory. (At this point it seem especially worthwhile to show how better results are available from statistical software.)

Next, some courses introduce exponential distributions, which are widely used in applications and are in many respects simpler to handle than normal distributions. That can lead to a discussion of other gamma family distributions. If the course has any kind of Bayesian flavor, beta distributions are often discussed as natural prior distributions for binomial success probabilities.

The specific distributions discussed later in the course depend on the purpose of the course in a theoretical or applied program. It is not possible in a single course to deal with all of the distributions and relationships among them that are displayed on your link. From there on there seems to be no traditional order as various objectives are pursued.

Any answer will be a matter of opinion, but I have taught lots of courses using what I believe to be a fairly standard order of presentation. I think there are good reasons for it and will discuss some of them.

Many elementary probability courses start with empirical discrete distributions. Proportions of various colors of candy bits in a large package of M&M's Skittles, or whatever. Some combinatorial material provides a basis for a few elementary distributions. Some basic rules of of probability are discussed.

After that and a discussion of tossing fair coins it is natural to get into a discussion of binomial distributions, which can involve some of the combinatorial arguments and probability rules. Also, a proof or discussion of the Law of Large numbers often appears at this point.

Next, depending on the level and applied nature of the course, it may be natural to discuss Poisson distributions as a limiting case of binomial one, and geometric and negative binomial distributions as waiting times for events already discussed in a binomial context. and to consider hypergeometric distributions as a generalization of binomial distributions where trials are not independent.

At some point a bridge needs to be crossed to discuss how continuous distributions differ fundamentally from discrete ones. Often starting with a brief mention of uniform distributions because of their mathematical simplicity, it is customary to spend a lot of time on normal distributions, because of their widespread use in applications, and because the Central Limit Theorem shows (or illustrates) convergence to normal.

Then a discussion of using normal distributions to approximate binomial probabilities seems mandatory. (At this point it seem especially worthwhile to show how better results are available from statistical software.)

Next, some courses introduce exponential distributions, which are widely used in applications and are in many respects simpler to handle than normal distributions. That can lead to a discussion of other gamma family distributions. If the course has any kind of Bayesian flavor, beta distributions are often discussed as natural prior distributions for binomial success probabilities.

The specific distributions discussed later in the course depend on the purpose of the course in a theoretical or applied program. It is not possible in a single course to deal with all of the distributions and relationships among them that are displayed on your link. From there on there seems to be no traditional order as various objectives are pursued.