You have a continuous random variable X, for which the mean µ equals 2.71.

You apply the transformation X * = 5 - 3X to the values of the random variable.

What is the mean of the transformed variable?

Since the random variable x is continuous, we can make use of linear operator

E (X*) = E (5 - 3X)

X * = E (5) - E (3X)

X * = 5 - 3E (X)

X * = 5 - 3 (2.71)

X * = - 3.13

The mean of the transformed variable is - 3.13.