Question

If variance of random variable x is 23, then what is the variance of 2x+10

Answer 1

uppose X is random variable with mean 'm' and variance 'v'. How does Y=aX+b look like? Let's consider the effect of scaling i.e. multiplication by 'a'. As is very obvious, the scaling just magnifies the data. When you are calculating the variance, you actually sum over the square of difference between a data points and the mean. So, you may see that multiplying by a factor 'a' will result into scaling the variance by a2a2.
If you look at the effect of adding 'b' i.e. shifting the whole data. You may notice that that has no effect at the variance because the variance tells us about the scattered-ness of the data about mean. So, when you shift the whole data, you are shifting the mean as well. So, the degree of dispersion is unchanged.
In nutshell, V(aX+b) =a2V(X)a2V(X).
And using this, one may easily see that V(2X+10)=4V(X)=92V(2X+10)=4V(X)=92.

Answer 2

Step-by-step explanation:

var(x) =23

var(x)= (2x+10)

= (2)^2 var(x)

= 4 ×23

= 92