Question

For a distribution the mean is 10, variance is 16, y =1 and ß, is 4. Find the
first four moments about the origin. Comment on the nature of distribution

​

Answer 1

Mean = 1

′ =10, variance = 2 =16, coefficient of skewness = 1 = +1, coefficient of kurtosis is 2 = 4.

First moment about the origin is

Mean = 1

′ = 10.

Next,

= 2 = 16 =

∑

2

− (

∑

)

2

.

Second moment about the origin is

2

′ =

∑

2

= 2 + 1

2 = + (

∑

)

2

= 16 + 102 =

Coefficient of skewness is +1:

1 = +1 =

3

2

3

2

→ 3 = 2

3

2 = 16

3

2 = 64

Coefficient of kurtosis is 4:

2 = 4

4

2

2 = 4 → 4 = 4(16)

2 = 1024

Third moment about the origin is

3

′ = 3 + 321

′ + 1

′ 3 = 64 + 3(16)(10) + 103 =

Fourth moment about the origin is

4

′ = 4 + 431

′ + 622

′ + 1

′ 4 = 1024 + 4(64)(10) + 6(16)102 + 104 =

It is a positively skewed distribution.

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