Probability & Statistics for Engineers & Scientists Lecture Notes PDF
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These lecture notes cover core concepts in probability and statistics, including sample spaces, random variables, and discrete probability functions. The document includes examples and definitions to explain complex topics, making it suitable for students studying engineering or science-related disciplines.
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Sample Space (S) S = {HH, HT, TH, TT} S = {DDD, DDN, DND, DNN, NDD, NDN, NND, NNN}. n(S) = 23 = 8 Example Random Variable ❑ Types of Random Variables ❑ Discrete Random Variable: X= {0, 1, 2}. ❑ Continuous Random Variable: 0≤X≤1 An experiment involves tossing a pair of dic...
Sample Space (S) S = {HH, HT, TH, TT} S = {DDD, DDN, DND, DNN, NDD, NDN, NND, NNN}. n(S) = 23 = 8 Example Random Variable ❑ Types of Random Variables ❑ Discrete Random Variable: X= {0, 1, 2}. ❑ Continuous Random Variable: 0≤X≤1 An experiment involves tossing a pair of dice, listing the elements the sample space S Random Variable 1. Tossing a coin twice. Find S S = {HH, HT, TH, TT}. n(S) = 4 X: is a random variable representing the number of appeared heads: X= {0, 1, 2} ❑ Types of Random Variables ❑ Discrete Random Variable: X= {0, 1, 2}. ❑ Continuous Random Variable: 0≤X≤1 Discrete Probability Distributions Function (pdf) Tossing a coin twice: S = {HH, HT, TH, TT}. n(S) = 4. Discrete Probability Distributions Function (pdf) Tossing a coin 3 times: S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}. n(S) = 8. Discrete Cumulative Distribution Function (cdf) Tossing a coin twice, X: is a RV => # of H S = {HH, HT, TH, TT}. n(S) = 4. X= {0, 1, 2}. 0≤𝑥
