10. Incorrect. The answer is true not false

 

Since y = x4 + 1 the relationship between the values y and x of the random variables y and x is given by:

 

y = x4 +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.