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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

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2 Answers

Recall that, in general,

mean(a*X+b) = a*mean(X)+ b  


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.

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