he length of time, in minutes, for and airplane to obtain clearance for take off at a certain airport is a random variable Y=3X-2, where x has the density funct

Question

what is the probabloty and the mean and variance of the above question

Answer 1

Recall that, in general,

mean(a*X+b) = a*mean(X)+ b  

and

std.deviation(a*x+b) = a*std.deviation(X)

It should also be intuitive, in the sense that multiplying a random variable by a stretches it (if |a|>1) or

shrinks it (if |a|<1) so that the standard deviation is greater or smaller, respectively. Adding a constant b only moves the possible values for the random variable X forward or backward, but does not change their position with respect to the mean and therefore  the constant "b" factor is irrelevant when computing variance or standard deviation.

Answer 2

It's the mean of the density function multiplied by 3, and then you subtract 2 from that number.

The standard deviation is the variance from the density function x3