Question

8. If u and u are the first two moments of the distribution about certain number then
second moment M2 of the distribution about the arithmetic mean is given by (1)
(A) -(u;)?
(B) 2u - u
(C) u + (u;)?
(D) x + 2(47)​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

option C is correct,m2 = m'2 - (m'1)^2

Correct Question

If m'1 and m'2 are the first two moments of the distribution about certain number then

second moment m2 of the distribution about the arithmetic mean is given by

(A) m'1

(B) 2m'1 - m1

(C) m'2 - (m'1)^2

(D) m2 + 2m1

Given

• m'1 and m'2 are the first two moments of the distribution about certain number

To find

• the correct expression for second Central moment

Solution

we are provided with first to random moments of a distribution about any arbitrary number and are asked to find the expression for second central moment of the distribution.

we know that moments are of two types raw moments and central moments, as well a random moment is critically associated with any random number of the distribution where as a central moment is estimated by making the arithmetic mean of the distribution as a key point.

from the standard equation to estimate the second Central moment (moment about the arithmetic mean) we can write,

second central moment = m'2 - (m'1)^2

or, m2 = m'2 - (m'1)^2

option C is correct.