lecture 10 - MGCR 271 Business Statistics Probability...

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MGCR 271 Business Statistics Ramnath Vaidyanathan Probability (Chapter 5)
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A coin is fipped 10 times. Each outcome is either a head or a tail. What is the probability that the number oF tails among the 10 fips is 5? Assume that the coin is a Fair one.
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A coin is fipped 10 times. Each outcome is either a head or a tail. What is the probability that the number oF tails among the 10 fips is 3? Assume that the coin is a Fair one.
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The result of any single coin toss is random. But the result over many tosses is predictable, as long as the trials are independent (i.e., the outcome of a new coin flip is not influenced by the result of the previous flip). First series of tosses Second series The probability of heads is 0.5 = the proportion of times you get heads in many repeated trials. http://bcs.whfreeman.com/pbs2e
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Probability Outcome Sample Space Event Random Variable
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A basketball player shoots three free throws. What are the possible sequences of hits (H) and misses (M)? H H H - HHH M M M - HHM H - HMH M - HMM S = { HHH, HHM, HMH, HMM, MHH, MHM, MMH, MMM } Note: 8 elements, 2 3 A basketball player shoots three free throws. What is the number of baskets made? S = { 0, 1, 2, 3 } Sample Space A basketball player shoots three free throws. What is the sample space?
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A random variable is a variable whose value is a numerical outcome of a random phenomenon. “A basketball player shoots three free throws. We deFne the random variable X as the number of baskets successfully made.” Discrete Random Variable : ±inite number of possible values. Continuous Random Variable : All values in an interval . Random Variable
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Finite sample spaces deal with discrete data — data that can only take on a limited number of values. These values are often integers or whole numbers. The individual outcomes of a random phenomenon are always disjoint. Hence, the probability of any event is the sum of the probabilities of the outcomes making up the event (addition rule). Throwing a die: S = {1, 2, 3, 4, 5, 6} Discrete Random Variables
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Statistics Probability Entity Outcome Population Sample Space Sample Event Property Random Variable
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S = {Head, Tail} P (head) + P (tail) = 0.5 + 0.5 =1 P (sample space) = 1 Coin Toss Example: S = {Head, Tail} Probability of heads = 0.5 Probability of tails = 0.5 Probability Rules Probability of getting a Head = 0.5 We write this as: P (Head) = 0.5 P (neither Head nor Tail) = 0 P (getting either a Head or a Tail) = 1 2) Because some outcome must occur on every trial, the sum of the probabilities for all possible outcomes (the sample space) must be exactly 1. P (sample space) = 1 1) Probabilities range from 0 ( no chance of the event ) to 1 ( the event has to happen ). For any event A,
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lecture 10 - MGCR 271 Business Statistics Probability...

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