ºÝºÝߣ

ºÝºÝߣShare a Scribd company logo
¦Ì
2
=
(x ¦Ì)2
n
2
=
x2
n
¦Ì2
s2
s2
=
(x x)2
n 1
s2
=
x2
( x)2
n
n 1
s
s
n
s2 1
n1
+
1
n2
s1
2
n1
+
s2
2
n2
¦Ì
¦Ì
¦Ì
t =
x ¦Ì0
s
n
¦Ì
¦Ì ¦Ì
¦Ì ¦Ì
¦Ì ¦Ì
¦Ì ¦Ì
x = 0.0508
s2
=
(x x)2
n 1
=
(0.051 0.0508)2
+ (0.0505 0.0508)2
+ etc...
6
= 9.15 10 7
s = s2
= 9.56 10 4
t =
x ¦Ì0
s
n
=
0.0508 0.05
9.56 10 4
7
= 2.17
¦Ì
¦Ì ¦Ì
¦Ì ¦Ì ¦Ì ¦Ì ¦Ì ¦Ì
t =
x1 x2
s2 1
n1
+
1
n2
t =
x1 x2
s1
2
n1
+
s2
2
n2
¦Ì ¦Ì
¦Ì ¦Ì
¦Ì ¦Ì
¦Ì ¦Ì
t =
x1 x2
s1
2
n1
+
s2
2
n2
=
700 668
212
12
+
302
6
= 2.342
2
=
(O E)2
E
2
=
(O E)2
E
=
(143 155.25)2
155.25
+
(60 51.75)2
51.75
+
(55 51.75)2
51.75
+
(18 17.25)2
17.25
= 2.519
2
=
(O E)2
E
=
(1 2.778)2
2.778
+ 2
(2 2.778)2
2.778
+ 4
(3 2.778)2
2.778
+ 2
(4 2.778)2
2.778
= 2.72
#1 +#3
#1 +#2 +#3 +#4
#1 +#3
#1 +#2 +#3 +#4
#1 +#2( )
E =
(#1 +#3 )(#1 +#2 )
#1 +#2 +#3 +#4
=
(row total)(column total)
grand total
2
=
(O E)2
E
E =
(row total)(column total)
grand total
=
(495)(490)
1960
=123.75
2
=
(O E)2
E
=
(113 123.75)2
123.75
+
(113 124)2
124
+
(110 124.26)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(A and B)
P(B)
P(A | B) =
P(B | A) P(A)
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)
P(B)
=
0.125
0.5
0.25
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) = (0.7 0.5) + (0.3 1) = 0.65
P(W = Zz | S = Z) =
0.5 0.7
0.65
= 0.538
P(X = m) =
n! pm
(1 p)(n m)
m! (n m)!
P(1 boy of 5 children) =
5! 0.51
0.54
1! (4)!
= 0.15625
P(X = m) =
e np
(n p)m
m!
Statistics Cheatsheet by MIT
Statistics Cheatsheet by MIT

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Statistics Cheatsheet by MIT

  • 1. ¦Ì 2 = (x ¦Ì)2 n 2 = x2 n ¦Ì2 s2 s2 = (x x)2 n 1 s2 = x2 ( x)2 n n 1 s s n s2 1 n1 + 1 n2 s1 2 n1 + s2 2 n2
  • 2. ¦Ì ¦Ì ¦Ì t = x ¦Ì0 s n ¦Ì ¦Ì ¦Ì ¦Ì ¦Ì ¦Ì ¦Ì ¦Ì ¦Ì x = 0.0508 s2 = (x x)2 n 1 = (0.051 0.0508)2 + (0.0505 0.0508)2 + etc... 6 = 9.15 10 7 s = s2 = 9.56 10 4 t = x ¦Ì0 s n = 0.0508 0.05 9.56 10 4 7 = 2.17 ¦Ì ¦Ì ¦Ì ¦Ì ¦Ì ¦Ì ¦Ì ¦Ì ¦Ì
  • 3. t = x1 x2 s2 1 n1 + 1 n2 t = x1 x2 s1 2 n1 + s2 2 n2 ¦Ì ¦Ì ¦Ì ¦Ì ¦Ì ¦Ì ¦Ì ¦Ì t = x1 x2 s1 2 n1 + s2 2 n2 = 700 668 212 12 + 302 6 = 2.342 2 = (O E)2 E
  • 4. 2 = (O E)2 E = (143 155.25)2 155.25 + (60 51.75)2 51.75 + (55 51.75)2 51.75 + (18 17.25)2 17.25 = 2.519 2 = (O E)2 E = (1 2.778)2 2.778 + 2 (2 2.778)2 2.778 + 4 (3 2.778)2 2.778 + 2 (4 2.778)2 2.778 = 2.72 #1 +#3 #1 +#2 +#3 +#4 #1 +#3 #1 +#2 +#3 +#4 #1 +#2( ) E = (#1 +#3 )(#1 +#2 ) #1 +#2 +#3 +#4 = (row total)(column total) grand total 2 = (O E)2 E
  • 5. E = (row total)(column total) grand total = (495)(490) 1960 =123.75 2 = (O E)2 E = (113 123.75)2 123.75 + (113 124)2 124 + (110 124.26)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(A and B) P(B) P(A | B) = P(B | A) P(A) P(B)
  • 6. 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) P(B) = 0.125 0.5 0.25 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) = (0.7 0.5) + (0.3 1) = 0.65 P(W = Zz | S = Z) = 0.5 0.7 0.65 = 0.538 P(X = m) = n! pm (1 p)(n m) m! (n m)! P(1 boy of 5 children) = 5! 0.51 0.54 1! (4)! = 0.15625 P(X = m) = e np (n p)m m!