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))
3 answers