Exercise 7. Let & be a real random variable whose c.d.f is Fε. 1. Find the c.d.f's of the following random variables in terms of F: • S=11- n = In() (assuming § > 0). 0 = exp(). 1 2. Suppose that is normally distributed with mean μ and variance o², i.e its p.d.f is given by 1 f(x) = e (x-2)² 202 2πσ (a) What is the p.d.f of (= (b) Find the p.d.f of C (folded normal distribution). Activate Windows

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Exercise 7. Let & be a real random variable whose c.d.f is Fε.
1. Find the c.d.f's of the following random variables in terms of F:
•
S=11-
n = In() (assuming § > 0).
0 = exp().
1
2. Suppose that is normally distributed with mean μ and variance o², i.e its p.d.f
is given by
1
f(x) =
e
(x-2)²
202
2πσ
(a) What is the p.d.f of (=
(b) Find the p.d.f of C (folded normal distribution).
Activate Windows
Transcribed Image Text:Exercise 7. Let & be a real random variable whose c.d.f is Fε. 1. Find the c.d.f's of the following random variables in terms of F: • S=11- n = In() (assuming § > 0). 0 = exp(). 1 2. Suppose that is normally distributed with mean μ and variance o², i.e its p.d.f is given by 1 f(x) = e (x-2)² 202 2πσ (a) What is the p.d.f of (= (b) Find the p.d.f of C (folded normal distribution). Activate Windows
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