Three things I learned my 1st day studying Statistics

How to describe easily a random experiment

Photo by Ruthson Zimmerman on Unsplash

What I learned

1. How to identify a random experiment

To identify a procedure as random experiment, it should have the following characteristics:

  1. It should be repeatable
  2. Its result is uncertain
  3. When know all the possible results

Its obvious that by definition when identifying a random experiment we also identify its sample space.

So the procedure ‘check out the products at the end of a construction pipeline to be quality approved’ can be identified as a random experiment, because: a) its a repeatable procedure b) we can not no its outcome before it happens, c) we know that the possible outcomes are ‘approved’ or ‘not approved’.

In the language of mathematics point c can be written like this:

Ω = {approved, not approved}

Using simplified symbols:

Ω = {a, n}

This way of symbolizing the sample space comes along the identification of a random experiment.

Useful terminology

Sample space: all the possible outcomes of a random experiment

Sample point: every possible outcome of a random experiment

Event: a subset of the sample space

2. How to characterize the sample space

Once we have found which the sample space is (identified its elements), we should characterize it as finite, countably infinite or continuous.

This type of characterization is about our ability to count the elements of the sample space. In the cases of finite and countably infinite sample space we are able to count the elements of the sample space. In the case of continuous sample space though we are not able to count its elements.

Finite and countably infinite sample spaces are also called discrete sample spaces. Finite sample spaces are easy to spot because you can count their elements even by hand. Countably infinite sample spaces are difficult to recognise by counting their elements by hand. Countably infinite sample spaces still countable though as, by mathematical definition, each one of their elements can be conjugated to a different natural number.

Examples:

Finite sample space: In our previous example (products quality check) the sample space has two elements (N(Ω)=2) and it is finite.

Countably infinite sample space: When the sample space is countably infinite, it means that every element of the sample space can be matched to a different natural number. For example, when we identify the sample experiment ‘Count how many defective products are produced by pipeline “A” in a day’ we identify the sample space to be Ω = {1,2,3,…}, which is countably infinite.

Continuous sample space: When we identify the random experiment ‘Count the time when the athlete will cross the finish line after the start of the start of the race’, we identify the sample space to be Ω = [0, +∞), which is infinite sample space.

This difference in the ability to count the elements of the sample space is important when diving into more advanced aspects of the probability theory, for that we should characterize the sample space the time we identify it.

3. How to describe events using words

Let’s say we have identified the random experiment ‘Ride down the street and meet three different traffic lights’ with Ω={rrr, rrg, rgr, grr, rgg, grg, ggr, ggg} a finite sample space where ‘r’ stands for the red light and ‘g’ for the green light. Let’s say we have the events A={rrr, ggg}, B={rrg, ggr} and C={rrg}.

We can describe the event A by saying:

  • This is the event where all the traffic lights are the same color

We can describe the event B by saying:

  • This is the event where the first two traffic lights are the same color and the third one has different color from the first two.

We can describe the event C by saying:

  • This is the event where the first two traffic lights are red and the third traffic light is green.

About my learning journey

My goal is to learn a bit of Statistics everyday for the next 21 days. I am going to study the basics to solidify my knowledge on Statistics and build a strong background for more advanced Data Science concepts.

This challenge is part of a bigger one, the #66daysofdata challenge! To learn more about the #66daysofdata challenge click here and here.

Resource

Introduction in Probability and Statistics, George Papadopoulos, Gutenberg (in greek)

Biotechnology Graduate | Data Science Enthusiast | Europe | Greece