若随机变量ζ~N(2,0.16),
求:(1)P{1,2≤ζ≤2),
(2)P{∣ζ-2∣﹥0.8).(已知:Φ(2)=0.9772)
若随机变量ζ~N(2,0.16),
求:(1)P{1,2≤ζ≤2),
(2)P{∣ζ-2∣﹥0.8).(已知:Φ(2)=0.9772)
【正确答案】:(1)P{1.2≤ζ≤2)=Φ[(2-2)/0.4]-Φ[(1.2-2)/0.4] =Φ(0)-Φ(-2) =Φ(0)+Φ(2)-1 = 0.5+0.9772-1 =0.4772 (2)P{∣ζ-2∣﹥0.8}=1-P{1.2≤ζ≤2.8}=2-2Φ(2) =2-2×0.9772=0.0456.
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