Given that the variance of 𝑋 equals 28, find the variance of four 𝑋 plus nine.
We need to remember that this kind of variance has certain properties. One of those properties looks like this. The variance of 𝐴𝑋 plus 𝐵 is equal to 𝐴 squared times the variance of 𝑋. We can plug in 28 for the variance of 𝑋. And we can substitute the variance of four 𝑋 plus nine in place of 𝐴𝑋 plus 𝐵. When we do this, we see that the 𝐴 value is equal to four. So we plug in four for the 𝐴 value. Four squared times 28 equals 16 times 28, which equals 448.
The variance of four 𝑋 plus nine is equal to 448. We know this is true based on the properties of variances.