Question

How can mean, standard deviation, and variance assist in the description of a probability distribution?

Answer 1

Answer:

We know that the mean of the probability distribution explains that the area below the mean and area above the mean are equal. This means, the area below the mean of probability distribution is 50% or 0.5. Thus mean give us a judgement about exact half area of the distribution. The standard deviation and variance explains the variation of the distribution. By using standard deviation or variance, we can judge about the variation in the distribution. If we know the mean, standard deviation, and variance of the probability distribution, then we get the idea of shape of the distribution. By using standard deviation and variance, we can guess the nature of probability curve. Also, by using mean, standard deviation, and variance, we can find out different moments of the distribution. It can be helpful in finding different types of generating functions of probability distribution.