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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,
, where P(x) is the probabiliy mass function.
- For a continuous probability distribution, the mean s given by,
, 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.