Question

What is the significance of the mean of a probability​ distribution?

Answer 1

Answer:

Significance of the mean of a probability​ distribution.          

Step-by-step explanation:

• The mean of a probability distribution is the arithmetic average value of a random variable having that distribution.

• For a discrete probability distribution, the mean is given by, $\sum x_iP(x_i)$, where P(x) is the probabiliy mass function.
• For a continuous probability distribution, the mean s given by, $E(x) = \int x_if(x_i)$, where f(x) is the probability density function.
• Mean is a measure of central location of a random variable.
• It is the weighted average of the values that X can take, with weights given by the probability density function.
• The mean is known as  expected value or expectation of X.
• An important consequence of this is that the mean of any symmetric random variable (continuous or discrete) is always on the axis of symmetry of the distribution.
• For a continuous random variable, the mean is always on the axis of symmetry of the probability density function.