Question

The first four moments of a distribution about arithmetic mean are 0, 16, -64 and 160 , Standard deviation (S.D) of a distribution is...​

Answer 1

Answer:

here,first four moments of a distribution about arithmetic mean are 0, 16, -64 and 160 .

we using the property of Moments,

μ1=0,μ2=ρ²x

then,

here μ2=16

so,

ρ=4

Standard deviation (S.D) of a distribution is...​4

Step-by-step explanation:

Answer 2

Given,

μ₁ = 0

μ₂ = 16

μ₃ = -64

μ₄ = 160

To find,

Standard deviation of a distribution (σ)

Solution,

The standard Deviation (S.D.) of a distribution is 4.

We can find the standard deviation of distribution by using the properties of moments.

As we know that

μ₁ = 0

μ₂ = Variance (σ²)

Thus, μ₂ = 16

        σ² = 16

        σ = √16

        σ = 4

Hence, the Standard Deviation (S.D.) of a distribution is 4.