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 significance of the mean of a probability distribution is it gives the expected value of a discrete random variable.
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 mean of a probability distribution:
After conducting many trials of an experiment, as the number of trials increases, we get the relative frequency and the theoretical values closer to each other. On observation, we find that in a long term, we expect a value that is known as the average or mean. This is the expected value denoted by μ. To find μ, just add all the products obtained by multiplying each value of the random variable by its probability.
Thus, the significance of the mean of a probability distribution is that it gives the expected value of a discrete random variable.