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Lecture 2 - Iowa State University
Lecture 2 - Iowa State University

... has had a course in algebra should be at least semi-comfortable with (2.1) as simply some rather ugly function of x. As alluded to above, (2.1) is the probability density function (pdf) for the random variable X ~ N (  ,  ) . As a proper density function, it has units of [probability per unit leng ...
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... Use logical reasoning to check the reasonableness of your answer. The probability that one student chosen out of 100 does not have a cat or a dog for a pet is (100 – 63)% or 37%. The probability that two people chosen out of 100 have a cat or a dog for a pet should be greater than 37%. Since 61% > 3 ...
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... So, if you test positive, then there is only a 25% chance that you have the condition! This answer is initially surprising, but makes sense on reflection. There are two ways you could test positive. First, it could be that you have the condition and the test is correct. Second, it could be that you ...
Estimating Sums of Independent Random Variables
Estimating Sums of Independent Random Variables

Chapter 6 Active Learning Questions
Chapter 6 Active Learning Questions

... An event is considered “significant” if its probability is less than or equal to 0.05. Muhammad Ali’s professional boxing record included 56 wins and 5 losses. If one match is selected at random, would it be considered significant if the match selected were a loss? ...
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... large constant fraction of the vertices. The second-largest component was smaller by many orders of magnitude. This property is shared by Erdös-Rényi random graphs and by many other graph models. In this lecture, we will see (mostly) why Erdös-Rényi random graphs have this property. The large co ...
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... To get an O(lg n)-time algorithm for this search problem, we will need to eliminate half the input at each step. Note that finding the median in a sorted array A of length n is O(1), since the median is just A[n/2]. So let x1 = X[n/2] and y1 = Y [n/2], and let m be the median value we’re looking for ...
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College Mathematics two-way tables and conditional probability

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Honors Algebra 2 and Trig

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