University:
Massachusetts Institute of Technology
Course:
18.05 | Introduction to Probability and Statistics
Academic year:

2021
Views:

364

Pages:

2
Author:

Alexa Livingston

Statistical Analysis and Probability Mean x-bar = (sum of Xi) / n Standard Deviation s = sqrt [ sum (Xi - x-bar)^2 / (n - 1) ] Standard Error of the Mean SE_x = s / sqrt(n) Chi-Square chi-square = sum [ (o - e)^2 / e ] x-bar = sample mean n = sample size s = sample standard deviation (i.e., the sample-based estimate of the standard deviation of the population) o = observed results e = expected results sum = sum of all Chi-Square Table Degrees of Freedom p value 1 2 3 4 5 6 7 8 0.05 3.84 5.99 7.81 9.49 11.07 12.59 14.07 15.51 0.01 6.63 9.21 11.34 13.28 15.09 16.81 18.48 20.09 Degrees of freedom are equal to the number of distinct possible outcomes minus one. Laws of Probability If A and B are mutually exclusive, then: P(A or B) = P(A) + P(B) If A and B are independent, then: P(A and B) = P(A) x P(B) Hardy-Weinberg Equations p^2 + 2pq + q^2 = 1 p + q = 1 p = frequency of allele 1 in a population q = frequency of allele 2 in a population Metric Prefixes Factor Prefix Symbol 10^9 giga G 10^6 mega M 10^3 kilo k 10^-1 deci d 10^-2 centi c 10^-3 milli m 10^-6 micro u 10^-9 nano n 10^-12 pico p Mode = value that occurs most frequently in a data set Median = middle value that separates the greater and lesser halves of a data set Mean = sum of all data points divided by number of data points Range = value obtained by subtracting the smallest observation (sample minimum) from the greatest (sample maximum) Rate and Growth Rate dY/dt dY = amount of change dt = change in time Population Growth dN/dt = B - D B = birth rate D = death rate Exponential Growth dN/dt = rmax N N = population size K = carrying capacity rmax = maximum per capita growth rate of population Logistic Growth dN/dt = rmax N (K - N) / K Simpson's Diversity Index Diversity Index = 1 - sum [ (n / N)^2 ] n = total number of organisms of a particular species N = total number of organisms of all species Water Potential (Psi) Psi = Psi_P + Psi_S Psi_P = pressure potential Psi_S = solute potential The water potential will be equal to the solute potential of a solution in an open container because the pressure potential of the solution in an open container is zero. The Solute Potential of a Solution Psi_S = -iCRT i = ionization constant (1.0 for sucrose because sucrose does not ionize in water) C = molar concentration R = pressure constant (R = 0.0831 liter bars/mole K) T = temperature in Kelvin (C + 273) pH = -log[H+] Surface Area and Volume Surface Area of a Sphere SA = 4 pi r^2 Volume of a Sphere V = (4/3) pi r^3 r = radius Surface Area of a Rectangular Solid SA = 2(lh + 2lw + 2wh) Volume of a Rectangular Solid V = lwh l = length h = height w = width Surface Area of a Cylinder SA = 2 pi r h + 2 pi r^2 Volume of a Cylinder V = pi r^2 h s = length of one side of a cube Surface Area of a Cube SA = 6s^2 Volume of a Cube V = s^3 SA = surface area V = volume

Statistical Analysis and Probability Sheet

Related Documents

Recommended Documents

Description

Related Documents

Almost There!

Free up your schedule!

Take 5 seconds to unlock