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Karo-lina-s [1.5K]
3 years ago
15

In the notation below, X is the random variable, c is a constant, and V refers to the variance.

Mathematics
1 answer:
Volgvan3 years ago
6 0

Answer:

-V(X + c) = V(X) + c

Step-by-step explanation:

Using the propierties of the variance:

  • <em>The variance of a constant is zero:</em>

<em></em>

<em>Var(k)=0</em>

<em></em>

Where k is an arbitrary constant. So:

-V(c) = 0 is true.

  • <em>If all values are scaled by a constant, the variance is scaled by the square of that constant: </em>

<em></em>

<em>Var(kX)=k^2V(X)</em>

<em></em>

Where k is an arbitrary constant. Therefore:

-V(cX) = c2 V(X) is true.

  • <em>Variance is invariant with respect to changes in a location parameter. That is, if a constant is added to all values of the variable, the variance is unchanged: </em>

<em></em>

<em>Var(X+k)=V(X)</em>

<em></em>

Where k is an arbitrary constant. Hence:

-V(X + c) = V(X) + c is not true.

<em></em>

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