Description
1 Definitions
1) The CDF of X is defined as,
FX(x) = Pr(X ≤ x)
2) The PDF of X is defined as, (1.1)
d
pX(x) = FX(x) dx
3) Let X ∼ N(µ,σ2). Then the Q function is defined as, (1.2)
Q(x) = Pr(X > x), x ≥ 0
2 Problems
1. Find (1.3)
Pr(|X − µ| ≤ kσ)
in terms of Q function.
2. Find (2.0.1.1)
Pr(X ≤ x, |X − µ| ≤ kσ)
in terms of FX(x)
3. Find (2.0.2.1)
FX (x| |X − µ| ≤ kσ)
4. Find (2.0.3.1)
pX (x| |X − µ| ≤ kσ) (2.0.4.1)
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