SOME SPECIFIC PROBABILITY DISTRIBUTIONS IGURE 3. Normal pdf and cdf Probability Density Function Cumulative distribution Function 08 1.4. Evaluating probability statements with a normal random variable. If x NN(u, 02) N(0,1) E(SOME SPECIFIC PROBABILITY DISTRIBUTIONS 3 Figure 3. Normal pdf and cdf −10 −5 0 5 10 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 Probability Density Function X f(X) −10 −5 0 5 10 0 0.2 0.4 0.6 0.8 1 Cumulative Distribution Function X F(X) 1.4. Evaluating probability statements with a normal random variable. If x ∼ N(µ,σ2) then, Z = X−µ σ ∼ N(0, 1) E (Z) = E  X−µ σ  = 1 σ · (E(X) − µ)=0 V ar (Z) = V ar  X−µ σ  = 1 σ2 V ar(X − σ) = σ2 σ2 = 1 (3)