The first four central moments (μ1, μ2, μ3, μ4) of a distribution are 0, 2.5, 0.7, and 18.75 respectively. Calculate the coefficient of skewness β1 of the distribution.

Consider the following statements regarding statistical distributions: 1. A symmetric distribution must have μ3 = 0. 2. μ3 = 0 implies the distribution is symmetric. 3. Kurtosis is independent of location but not of scale. Which of the above statements is/are correct?

The first four moments of a distribution about X = 2 are -2, 12, -20, and 100. Then the fourth central moment μ4 equals: