Question

Дисперсия случайной величины X равна пяти. Найдите дисперсию величины: 3X+6

Answer 1

D(3X+6)=D(3⋅X)+D(6)=32⋅D(X)+0=9⋅5=45

Answer 2

To find the variance of a new random variable, which is given by 3X + 6, we can use the following property:

If Y = aX + b, where a and b are constants, then the variance of Y is equal to a^2 times the variance of X.

In this case, Y = 3X + 6. We know that the variance of X is 5 (given as 5). Now, we need to find the variance of Y.

Variance of Y = (a^2) * Variance of X Variance of Y = (3^2) * 5 Variance of Y = 9 * 5 Variance of Y = 45

Therefore, the variance of the random variable 3X + 6 is 45.