$X \sim N (1,4) ;\, Y= 2X+1;$
And now does $Y$ have $N(1\times2+1,\, 2\times4+1) = N(3,9)$ ?
Is it valid? And if so why ? Or how do I get y's distribution?
Because when I run the following in R, it yields
x = dnorm(1,1,4) #  0.09973557 y = dnorm(3,3,9) #  0.04432692