Question

The first three moments of a distribution about the value 2 of the variable are 1, 16 and -40. Show that the mean is 3, the variance 15 and m3 is -86. Also show that the first three moments about x=0 are 3, 24 and 76.

          The first three moments of a distribution about the value 2 of the variable are 1, 16 and -40.
Show that the mean is 3, the variance 15 and m3 is -86. Also show that the first three moments
about x=0 are 3, 24 and 76.

Added by Raquel R.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Sagar Singh

11/10/2021

Step 1

We are given that $\mu_1 = 1$, $\mu_2 = 16$, and $\mu_3 = -40$. Let $m_i$ be the $i$-th moment about the mean. Let $\bar{x}$ be the mean. The first moment about the value 2 is given by: $\mu_1 = E(X - 2) = E(X) - 2 = \bar{x} - 2 = 1$ Therefore, $\bar{x} = 1 + 2 = Show more…

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The first three moments of a distribution about the value 2 of the variable are 1, 16 and -40. Show that the mean is 3, the variance 15 and $m_3$ is -86. Also show that the first three moments about $x=0$ are 3, 24 and 76.