Exercise 7. Let xi be a real random variable whose c.d.f is F_(xi ).
Find the c.d.f's of the following random variables in terms of F_(xi ) :
zeta =|xi |.
eta =ln(xi ) (assuming xi >0 ).
heta =exp(xi ).
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Suppose that xi is normally distributed with mean mu and variance sigma ^(2), i.e its p.d.f is given by
f(x)=(1)/(sqrt(2pi )sigma )e^(-((x-mu )^(2))/(2sigma ^(2))).
(a) What is the p.d.f of zeta :=(xi -mu )/(sigma ).
(b) Find the p.d.f of |zeta | (folded normal distribution).
Exercise 7. Let & be a real random variable whose c.d.f is Fs
1. Find the c.d.f's of the following random variables in terms of Fs:
131=5. n = ln($) (assuming$> 0) .0 = exp($).
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2. Suppose that & is normally distributed with mean and variance o2, i.e its p.d.f is given by 1 20
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(a) What is the p.d.f of ( := $-. (b) Find the p.d.f of || (folded normal distribution)