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I am dealing with a random variable which is a transformation of another random variable of the form:

[tex] Y:=aX^b+c [/tex]

The pdf of the random variable

If I want to know the median value of Y ,[itex]Y_{M}[/itex], then given that median of X is known and equal to say [itex]X_{M}[/itex] is [itex]Y_{M}[/itex] going to be equal to: [itex]a(X_{M})^b+c[/itex] ?

I suppose I could generate samples from the distribution of Y and use empirical density function to determine approx. quantiles but I'd rather go down the analytical route if possible

Thanks in advance!

[tex] Y:=aX^b+c [/tex]

The pdf of the random variable

*X*is known and for the sake of example let it be exponential distribution or any other distribution with known and commonly available quantile function.If I want to know the median value of Y ,[itex]Y_{M}[/itex], then given that median of X is known and equal to say [itex]X_{M}[/itex] is [itex]Y_{M}[/itex] going to be equal to: [itex]a(X_{M})^b+c[/itex] ?

I suppose I could generate samples from the distribution of Y and use empirical density function to determine approx. quantiles but I'd rather go down the analytical route if possible

Thanks in advance!

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