Functions of the standard normal

The random variable 𝑋 has a standard normal distribution. Find the PDF of the random variable 𝑌, where:

𝑌=5𝑋−7.

ANSWER: 𝑓𝑌(𝑦)=1/5𝑓_𝑋((𝑦+7)//5)

𝑌=𝑋^2−2𝑋. For 𝑦≥−1,

ANSWER: (𝑓_𝑋(1+√(𝑦+1))+𝑓_𝑋(1−√(𝑦+1)))/(2√(𝑦+1))

or

ANSWER: (𝑓_𝑋(1+sqrt(𝑦+1))+𝑓_𝑋(1−sqrt(𝑦+1)))/(2*sqrt(𝑦+1))

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