2. Let P(x):
x x . (10 pts)
2
Find
a. P (1)
b. P (4)
c. n, P(n)
d. n,P(n)
a)P(x>−1)=1−P(x+24≤−1+24)=1−P(Z≤12)=1−ϕ(0.5)=1−0.69146=0.30854b)P(x=0)=P(x+24≤0+24)=P(Z=1)=0c)P(x<0)=P(x+24<0+24)=1−P(Z<1)=ϕ(1)=0.84134d)P(−2<x<0)=P(−2+24<x+24<0+24)=P(0<Z<22)=ϕ(1)−ϕ(0)=0.84134−0.5=0.3413a)\\ P(x>-1)= 1-P(\frac{x+2}{\sqrt4}≤\frac{-1+2}{\sqrt4})\\ = 1-P(Z≤\frac{1}{2})= 1- \phi(0.5)\\ =1-0.69146=0.30854\\ b)\\ P(x=0)= P(\frac{x+2}{\sqrt4}≤\frac{0+2}{\sqrt4})\\ =P(Z=1)= 0\\ c)\\ P(x<0)= P(\frac{x+2}{\sqrt4}<\frac{0+2}{\sqrt4})\\ = 1-P(Z<1)=\phi(1)\\ =0.84134\\ d)\\ P(-2<x<0)= P(\frac{-2+2}{\sqrt4}<\frac{x+2}{\sqrt4}<\frac{0+2}{\sqrt4})\\ = P(0<Z<\frac{2}{2})= \phi(1)-\phi(0)\\ =0.84134-0.5\\ =0.3413a)P(x>−1)=1−P(4x+2≤4−1+2)=1−P(Z≤21)=1−ϕ(0.5)=1−0.69146=0.30854b)P(x=0)=P(4x+2≤40+2)=P(Z=1)=0c)P(x<0)=P(4x+2<40+2)=1−P(Z<1)=ϕ(1)=0.84134d)P(−2<x<0)=P(4−2+2<4x+2<40+2)=P(0<Z<22)=ϕ(1)−ϕ(0)=0.84134−0.5=0.3413
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