Question

2. Let P(x):

x  x . (10 pts)

2

Find

a. P (1)

b. P (4)

c.  n, P(n)

d.  n,P(n)

Answer 1

$a)\\ P(x>-1)= 1-P(\frac{x+2}{\sqrt4}≤\frac{-1+2}{\sqrt4})\\ = 1-P(Z≤\frac{1}{2})= 1- \phi(0.5)\\ =1-0.69146=0.30854\\ b)\\ P(x=0)= P(\frac{x+2}{\sqrt4}≤\frac{0+2}{\sqrt4})\\ =P(Z=1)= 0\\ c)\\ P(x<0)= P(\frac{x+2}{\sqrt4}<\frac{0+2}{\sqrt4})\\ = 1-P(Z<1)=\phi(1)\\ =0.84134\\ d)\\ P(-2<x<0)= P(\frac{-2+2}{\sqrt4}<\frac{x+2}{\sqrt4}<\frac{0+2}{\sqrt4})\\ = P(0<Z<\frac{2}{2})= \phi(1)-\phi(0)\\ =0.84134-0.5\\ =0.3413$