**10. Correct. The answer is true**

Since *y *= *x*^{4} + 1 the
relationship between the values *y* and
*x* of the random variables *y* and *x *is given by:

*y* = *x*^{4}+1 or
x = (*y*-1)^{1/4}, where *y* = 2, 17,
82, etc.

and the
real positive root is taken. Then the required probability function for *y* is given by

*g(y) = 2-(y-1)^(1/4) y *= 2, 17, 82, etc.

*g(**y) = 0* otherwise

using Theorem 2-1, p.44 in Schaum's Outlines Probability and Statistics.