Probability theory is one of the core topics of mathematicians and actuaries. As it may sound, it’s not an easy topic. Students normally find it very challenging to understand its core concepts. In this article, we will provide you with a basic introduction of probability theory. It’s a wide topic. We cannot cover all its concepts here. But the basics should serve you well.
History of probability theory.
The earliest known evidence of probability theory comes from Arab mathematicians in the 13th century. The modern probability theory has its origin in the 16th century when Gerolamo Cardano was studying the game of chance. Other contributors to this topic are Blaise Pascal and Pierre de Fermat.
Let’s start with a simple analogy that is mostly used when studying probability theory, the flipping coin example. This example is like the hello world code that every novice programmer must write when starting their programming journey. In the flip coin example. When one flips a coin, there is an equal chance that the head or tail might appear. Further, there is some randomness associated with this experiment. Basic probability definitions
A random event or experiment is an event whose outcome cannot be predicted with certainty. For the above-mentioned example, the event of flipping a coin is a random event.
For a random experiment, a sample space means the set of all the values of the random event that it can take. For the flipping coin example, the sample space is the head and tail
A random variable is a set of all the likely values the experiment could take. Note that the random variable does not deviate from the set of values that it could take. In probability theory, a random variable is often denoted by a capital letter RV. There are two types of random variables discrete RVs and continuous RVs. The difference lies in the type of numerical values each takes. Discrete random variables take discrete values and are always finite. Continuous variables take continuous values and can be infinite. Examples of continuous data could be height and weight.
We had meandered a lot before we arrived at one of the most critical terms of the discussion in this article. Probability implies the likelihood of something to happen. You have come across the words such as the probability that it will rain today is 60%. What do they imply? What they mean is that there is a 60% chance it will rain. It’s not certain, but it’s more likely to happen. It’s like probability is a game of chance. Probability always ranges from 0 to 1. A zero value implies that we are certain the event won’t happen while in the other extreme end, we are certain the event will happen.
The expectation of an RV is its center. In unprofessional terms, it’s the mean of the random variable. It’s often denoted as E(X), where X is the random variable.
Whereas the expectation captures the center of the random variable, the variance tries to quantify the spread of the distribution. In the business context, the variance could imply the risk. The variance is given as the average of the squared differences of the random variable and the expectation.
What our probability theory assignment solutions encompass
Joint probability distributions
Cumulative probability distributions
The central limit theorem
Expectations of random variables
The variance of random variables.
Probability theory assignment help
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