¦Ì
(x ¦Ì)2
s2 =
s
s n
2= n
s2
x2 2=n¦Ì2
x2 (x)2 n
(x x)2
n1 n1
s2 =
21 1
s n + n
s12 s2
n + n 1212
¦Ì
¦Ì ¦Ì
t = x ¦Ì0 s
n
¦Ì
¦Ì¦Ì
¦Ì¦Ì
¦Ì¦Ì
¦Ì ¦Ì
x = 0.0508
2
(x x)2 (0.051 0.0508)2 + (0.0505 0.0508)2 + etc… 7
s = s =
n1 = 6 s2 = 9.56 104
=9.1510
t = x ¦Ì0 = 0.0508 0.05 = 2.17 s 9.56104
n
¦Ì
¦Ì¦Ì
¦Ì¦Ì ¦Ì¦Ì ¦Ì¦Ì
7
t = x1 x2 t = x1 x2
2 1 1 s 12 s 2 2 sn+n n+n 1 2 1 2
¦Ì¦Ì
¦Ì ¦Ì
¦Ì¦Ì
¦Ì¦Ì
t= x1 x2
s12 s2 n+n
= 700668 =2.342 212 302
2 (O E)2
= E
12
12+ 6
2 (O E)2 (143155.25)2 (6051.75)2 (5551.75)2 (1817.25)2
= E = 155.25 + 51.75 + 51.75 + 17.25 =2.519
(O E)2 (12.778)2 (22.778)2 (32.778)2 (4 2.778)2 2
= E = 2.778 + 2 2.778 + 4 2.778 + 2 2.778 = 2.72
#1 +#3
#1+#2 +#3 +#4
#1 +#3 (#1+#2)
#1+#2 +#3 +#4
E = (#1 +#3 )(#1 +#2 ) = (row total)(column total)
#1 +#2 +#3 +#4 grand total
2 =(OE)2 E
E = (row total)(column total) = (495)(490) =123.75
grand total
2 (O E)2
= E =
1960
(113123.75)2 (113124)2 123.75 + 124
(110124.26)2
+ 124.26 + etc…= 91.73
P(A and B) = P(A) P(B)
P(A or B) = P(A) + P(B) P(A and B)
P(A|B)= P(AandB) P(A|B)= P(B|A)P(A)
P(B) P(B)
0.5 0.5 0.5 = 0.125 = P(A and B) = P(2 children = bb and 1st child bb)
P(B) = P(1st child = bb) = 0.5
P(2 children = bb | 1st child bb) = P(A | B) = P(A and B) = 0.125 0.25 P(B) 0.5
P(A|B)= P(B|A)P(A)
P(B)
P(S = Z |W = Zz) = 0.5
P(W = Zz) = 0.7
P(S=Z)=(0.70.5)+(0.31)=0.65
P(W =Zz|S=Z)=0.50.7=0.538 0.65
P(X=m)=n!pm (1p)(nm)
m!(n m)!
5!0.51 0.54
P(1 boy of 5 children) = 1!(4)! = 0.15625
P(X=m)=enp (np)m
m!