Question

The first four moments of distribution about x = 4 are 1, 4, 10, and 45. Calculate the variance.​

Answer 1

Answer:

16

Step-by-step explanation:

a) For a distribution, the mean is 10, variance is 16, coefficient of skewness is +1 and

coefficient of kurtosis is 4. Obtain the first four moments about the origin i.e., zero.

Comment upon the nature of distribution. (5)

b) Calculate the correlation coefficient for the following heights (in inches) of father

(X ) and their sons ) (Y : (5)

X : 65 66 67 67 68 69 70 72

Y : 67 68 65 68 72 72 69 71

Answer 2

The variance is 414.

Given: The first four moments of distribution about x = 4 are 1, 4, 10, and 45.

To find: We have to find the variance.

Solution:

The first four moments of distribution about x = 4 are 1, 4, 10, and 45.

The mean is-

$\frac{1 + 4 + 10 + 45}{4} = 15$

Deviation from mean is-

$15 - 1 = 14 \\ 15 - 4 = 11 \\ 15 - 10 = 5 \\ 45 - 15 = 30$

Sum of the squares of the deviation are-

${14}^{2} + {11}^{2} + {5}^{2} + {30}^{2} \\ = 196 + 121 + 25 + 900 \\ = 1242$

The total number of deviations is 4. So, n is equal to 4.

n-1 is equal to 4-1=3.

Thus variance will be-

$\frac{1242}{3} = 414$