Introduction to Discrete & Continuous Probability Distributions

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  ✅ 1. What is a Probability Distribution? A probability distribution describes how probabilities are distributed over the values of a random variable . Random Variable : A variable whose values are outcomes of a random phenomenon. ๐Ÿงฎ 2. Types of Probability Distributions Type Description GIS Example Discrete           Takes countable values  Number of landslides per year in a          valley Continuous          Takes infinite values over an                 interval Rainfall (mm), elevation, temperature  ๐Ÿ“Œ Discrete Probability Distributions ๐ŸŽฏ 3. Binomial Distribution ✅ Definition : Used when an experiment is repeated n times , and each trial has two outcomes : success or failure. ✅ Conditions : Fixed number of trials (n) Only two possible outcomes per trial (success/failure) Constant probability of success (p) Trials are in...
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Introduction to Statistics

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 Statistics is the science of collecting, organizing, analyzing, and interpreting data. It is all about data. First, we collect data. Data just doesn't appear, we collect it through surveys, experiment, or measuring and recording the information.

Once we get the data then we organize it and put it in order either ascending or descending order. This is the most common thing to be applied to data. The data can be put in table form or can be represented in graphical form. To check what the data tells us, we analyze the data. We find the mean, median, mode, range, or standard deviation of the data. So what statistics is all about it is all about collecting data and using it to help answer a question. So statistics is all about answering a question.

 Now what exactly is a good statistical question, well a statistical question is where you expect to get a variety of answers that is really big a variety of answers a whole range of answers you are not expecting just a couple different options and you are interested in the distribution and tendency of those answers.

One more thing about statistical questions don't get confused between a survey question and a statistical question for example if your statistical question was how much do sixth graders weigh well that's a statistical question but when you do the survey you're not going to ask people how much do sixth graders weight you're going to say how much do you weigh and you go to the next person how much do you weigh and then next person and in this way all the sixth graders you're going to serve it you ask them how much do you weigh and that would not be a statistical question but it's going to help us get data to answer the statistical question.

So with that let's get to our first example. Let's say your science teacher asks you to do an experiment about mice and she asks what is the weight of a mouse okay well first is this a statistical question and if so explain now if you remember from the definition statistical questions should be giving us a variety of answers they should be able to show us the distribution and tendency so we have to think well this question if I'm doing experiment with mice is it going to give me a variety of answers and the answer is yes it will because you can't expect all mice to weigh the same they're going to be different just like humans are going to weigh different, same with mice so our answer is yes because you would expect the weight of mice to vary. Let's try Part B okay Part B so we weigh a whole bunch of mice and we collected the data, so it looks kind of confusing it's hard to tell anything about the data right now. To get results from the data we analyze the data. We arrange the data in ascending order or descending order, or we make a table of the data to find out the frequency distribution of the data, to know how many counts fall in one group of measurement. We find the mean, mode, or median to find out about the average value of the data, where the center of the data lies. To find the amount of dispersion in the data we find its standard deviations. This is all about the analysis of the data. Then comes the interpretation of the data. Once you get the result of the analysis of the data you interpret the result. You explain the result and what is the result telling us about the statistical question.

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