Statistics Cheatsheet by MIT
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This document contains mathematical formulas and calculations related to probability and statistics. It includes formulas for variance, standard deviation, t-tests, chi-squared tests, conditional probability, binomial probability, and Poisson probability. An example calculates the probability of having 1 boy out of 5 children.
Statistics Cheatsheet by MIT
- 1. μ 2 = (x μ)2 n 2 = x2 n μ2 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. μ μ μ t = x μ0 s n μ μ μ μ μ μ μ μ μ 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 μ0 s n = 0.0508 0.05 9.56 10 4 7 = 2.17 μ μ μ μ μ μ μ μ μ
- 3. t = x1 x2 s2 1 n1 + 1 n2 t = x1 x2 s1 2 n1 + s2 2 n2 μ μ μ μ μ μ μ μ 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!