9/27/2013
H.W3
Central Limit
Theorem
H.W3 Report
1) Generate Histogram for Uniform Distribution data. N=150
Sum ary for uniform distribution
m
A nderson-Darling Normality Test
A -Squared
P-V alue <
Mean
StDev
V ariance
Skewness
Kurtosis
N
3
6
9
12
1.44
0.
1)
a) P(X>65)
z=
x 6569
=
=1.428
2.8
P(X>65) = P (z> -1.428) = 0.923
b) P(X>72)
z=
x 7269
=
=1.071
2.8
P(X>72) = P (z> 1.071) = 1-0.85769 = 0.14231
c) P(62<X<72)
z for 62=
x 6269
=
=2.5
2.8
P (z>-2.5) = 0.99379
P (z>1.071) = 0.14231
P (62<X72) = P (-2.5<Z
H.W (1) Graphs included
9/15/2013
1. Find P cfw_Z < 1.51.
P (z < 1.51) = 0.9345
Distribution Plot
Normal, Mean=0, StDev=1
0.4
Density
0.3
0.9345
0.2
0.1
0.0
0
X
93.45% of the random variables of X are less than 1.51.
2. Find P cfw_Z > 1.97.
P cfw_Z > 1.97
H.W 3C
E ( x )=1 0.6+2 0.4=1.4
E ( x 2) =12 0.6+22 0.4=2.2
2
2
E ( x ) =1.4 =1.96
2
v ( x )=E ( x 2 )E ( x ) =0.24
(X1, X2) = cfw_(1, 1), (1, 2), (2, 1), (2, 2)
X 1,1.5, 2
cfw_
x
a. P( =1) = Pcfw_(1,1) = .6*.6 = .36
P cfw_(1, 2) or (2, 1) = .6*.4+ .4*.6 =