Question

the S.D of a symmetric distribution is 5 .What must be the value of the fourth moment about the mean in the order that the distribution be A. Leptokurtic B. mesokurtic C. platykurtic.​

Answer 1

Answer:

the S.D of a symmetric distribution is 5 .What must be the value of the fourth moment about the mean in the order that the distribution be A. Leptokurtic B. plz mark my ans as brainiest plz

Answer 2

Given

• S.D of a symmetric distribution is 5

To find

• the value of the fourth moment so that,

1. the distribution be A. Leptokurtic
2. B. mesokurtic
3. C. platykurtic.

Solution

we know that the measurement of kurtosis is given by,

B = (m4)/(m2)^2

where m4 is the fourth Central moment and m2 is the second Central moment respectively.

For a distribution to be

1. leptokurtic, B should be greater than 3
2. mesokurtic, B should be equal to 3
3. Platykurtic, B should be less than 3

we have been provided with the standard deviation which is the square root of variance thus, we can write the variance of the distribution as, 5^2 or 25

we know that variance is the second Central moment therefore,

m2 = 25

substituting the values and applying the conditions we get,

leptokurtic

B > 3

or, (m4)/(25)^2 > 3 (simplifying)

or, m4 > 1875

mesokurtic

B = 3

or, (m4)/(25)^2 = 3

or, (m4)/625 = 3

or, m4 = 1875

Platykurtic

B < 3

or, (m4)/(25)^2 < 3

or, (m4)/625 < 3

or, m4 < 1875