Question

Find out standard deviation of y and r from the following data:3x=y ,4y=3x and standard deviation of x is 2​

Answer 1

Given:

3x = y, 4y = 3x and standard deviation of x is 2​

To find:

Find out the standard deviation of y and r from the following data: 3x = y, 4y = 3x and standard deviation of x is 2​

Solution:

From given, we have,

The standard deviation of x is 2.

⇒ σ = 2.

Variance = σ² = 2² = 4

∴ Var(x) = 4

3x = y

⇒ y = 3x

Var (y) = Var (3x)

⇒ Var (y) = 3 Var (x)

= 3 × 4

= 12

⇒ Var (y) = σ² = 12

∴ The standard deviation of y = σ = √12 = 2√3

4y = 3x

⇒ y = 3/4x

Var (y) = Var (3/4x)

⇒ Var (y) = 3/4 Var (x)

= 3/4 × 4

= 3

⇒ Var (y) = σ² = 3

∴ The standard deviation of y = σ = √3