What is the significance of the mean of a probability distribution?
Random sampling, as the name suggests is a very random method and it might be perfect or might even be biased.
Answer: The most significant role of probability distribution arises when random sampling does not give perfect data about the population.
Let us go through the explanation to understand better.
What Is a Probability Distribution?
A probability distribution is a statistics-based function that describes all the possible values that a random variable can take within a given set of ranges. This range is bound to be within a certain minimum and maximum possible values, but precisely where the possible value is likely to be plotted on the probability distribution depends on a number of factors. These factors include the distribution's mean (i.e., average), standard deviation, skewness.
Various types of the Probability distribution
There are many different types of probability distributions. Some of them are the normal distribution, chi-square distribution, binomial distribution, and Poisson distribution. The different probability distributions serve different purposes and represent different data generation processes. For example, the binomial distribution evaluates the probability of an event occurring several times over a given number of trials and given the event's probability in each trial.
Significance of the probability distribution:
It is an important and well-known method to collect raw data by random sampling since it gives no inherent bias in sampling. But this does not mean that all random samples are necessarily perfect. One random sample may give perfect data of the population while others may be completely off chance. Unfortunately, when looking at a sample, we never know how much it differs from the actual population, thus, this where the actual use of the probability distribution comes into the picture.