Determine the density function of Y X2 7X10 where X denotes

Determine the density function of Y = X^2 -7X+10 where X denotes the number of points thrown in a toss of a die whose faces are equally likely.

Solution

Let F(X)= Y be the given function.

We have that the density function f(x) is gievn as

f(x)=F`(x) =d/dx (Y) =d/dx(x^2-7x+10

=d/dx(x^2)-d/dx (7x) + d/dx(10) ( Because d/dx (x^n )= nx^(n-1) and d/dx(c) =0 where c is a constant)

=2x-7(1)+0

f(x)=2x-7

that is the required density function.