ISA 205 Study Guide - Midterm Guide: Sample Size Determination, Standard Score, Sample Space
28 Jun 2018
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Experiment: any process of observation with uncertain outcome
Probability: measure of chance that an experimental outcome will occur when experiment takes place
Sample space: set of all possible experimental outcomes; exper. outs in sample space = sample space outcomes
Conditions: (1) 0< P(E) < 1 if E never occurs P(E)=0, if E is certain to occur P(E)=1. (2) probabilities must = 1
3 methods: classical method (equally likely outcomes), relative frequency method (using the long run relative
frequency), subjective method (assessment based on experience/expertise)
Event = set of sample space outcomes probability of an event: sum of probabilities of sample space outcomes
Complement (Ā): the set of all sample space outcomes not in A. P(Ā) = 1-P(A)
Union: events that belong to either A or B or Both. A È B = A + B
Intersection: events that belong to both A and B. A B = A + B - AB∩
Mutually exclusive: if A and B have no sample space outcomes in common. P(A B) = 0∩
Addition Rule:
If A and B are mutually exclusive then probability that A or B (union) will occur is: P(AÈB) = P(A) + P(B)
If A and B are not mutually exclusive, probability is: P(AÈB) = P(A) + P(B) – P(A B)∩
Conditional probability: probability of event A, give that event B has occurred P(A|B)
P(A|B) = P(A B) / P(B) OR P(B|A) = P(A B) / P(A)∩ ∩
Independent: two events A and B are independent if P(A|B) = P(A) OR P(B|A)=P(B)
Multiplication Rule: two ways to calculate P(A B)∩probability A&B occur if independent
1. P(A B) = P(A) P(B|A) ∩P(A B) = P(A)*P(B)∩
2. P(A B) = P(B) P(A|B)∩
Random Variable: variable that assumes numerical values that are determined by the outcome of experiment
Discrete Random Variable: possible values can be counted or listed.
-number of defective units in batch of 20, listener rating on scale 1-5 in music survey
-sum p(x) = 1and p(x) > 0 no negatives
Continuous Random Variable: may assume any numerical value in 1+ intervals.
- waiting time for credit card authorization, interest rate charged on business loan
- area under f(x) = 1 and f(x) > 0 no negatives
mean/expected value of discrete X variance standard deviation
binomial experiment: (1) consists of n identical trials (2) each trial results in success or failure (3) probability of
success, p, is constant from trial to trial, q=1-p (4) trials are independent
probability of x successes in n trials; 0! = 1
if x is a binomial random variable with parameters n and p (so 1 = 1-p), then:
Mean m = n•p
Variance s2x = n•p•q
Standard deviation sx = square root n•p•q
Continuous probability distribution = probability curve = probability density function
f(x) is continuous such that (1) f(x)>0 for all x and (2) total area under f(x) curve = 1
distribution shapes: symmetrical rectangular (uniform dist), symmetrical bell shaped (normal dist), skewed
uniform distribution: NOTE: c<a<b<d rectangular
c and d numbers on real line (c<d), probability that x is any value
probability curve describing it btwn the values a and b (a<b) var = (d-c)^2 / 12
probability that x is any one number in continuous distribution = 0
endpoints c and d: width = d-c and height = 1/(d-c) area under curve must equal 1
find more resources at oneclass.com
find more resources at oneclass.com
Document Summary
Experiment: any process of observation with uncertain outcome. Probability: measure of chance that an experimental outcome will occur when experiment takes place. Sample space: set of all possible experimental outcomes; exper. outs in sample space = sample space outcomes. Conditions: (1) 0< p(e) < 1 if e never occurs p(e)=0, if e is certain to occur p(e)=1. (2) probabilities must = 1. 3 methods: classical method (equally likely outcomes), relative frequency method (using the long run relative frequency), subjective method (assessment based on experience/expertise) Event = set of sample space outcomes probability of an event: sum of probabilities of sample space outcomes. Complement ( ): the set of all sample space outcomes not in a. p( ) = 1-p(a) Union: events that belong to either a or b or both. Intersection: events that belong to both a and b. Mutually exclusive: if a and b have no sample space outcomes in common.
