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each value in a sample has been transformed by multiplying by 3 and then adding 10. if the original sample had a variance of 4, what is the variance of the transformed sample?

Respuesta :

nuhulawal20

Given that the original sample had a variance of 4, variance of the transformed sample is 36.

Given the data in the question;

  • Each value in a sample has been transformed by multiplying by 3
  • Then add 10
  • Original sample had a variance of 4

Now, Lets represent the original random variable by X  

So, Variance of X will be 4

Var(X) = 4

The Variance of the transformation is;

[tex]Y = 3X + 10[/tex]

By using property of variance [ derived from its definition]

[tex]Var(Y) = a^2Var(X)[/tex]

Here, X is the variable and "a" is the constant

We substitute

[tex]Var(Y) = 3^2\ * \ 4[/tex]

[tex]Var(Y) = 9\ *\ 4\\[/tex]

[tex]Var(Y) = 36[/tex]

Therefore, given that the original sample had a variance of 4, variance of the transformed sample is 36.

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