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Class Note for MATH 1313 with Professor Flagg at UH

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This 5 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Houston taught by a professor in Fall. Since its upload, it has received 21 views.

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Date Created: 02/06/15
b Find the event comprising the outcomes to which a value of 2 has been assigned by the random variable X c Find the probability distribution of the random variable X Notation The question in part b above can be summarized by this notation X 2 Example 3 LetX denote the random variable that gives the sum of the faces that fall uppermost when two dice are cast a What are the possible values assigned to the random variable b Find the event comprising the outcomes to which a value of 7 has been assigned by the random variable Math 1313 Class Notes 7 Section 81 Page 2 of5 c List the outcomes of the experiment in the event for which the random variable is assigned the value of 10 X10 Example 4 A survey was conducted by a technology firm among 1000 families to determine the distribution of televisions in average households Here are the results No0fTVs 0 1 2 3 4 5 6 FREQUENCYOFOUTCOME 10 230 295 325 116 20 4 Construct a probability distribution of the random variable X where X denotes the number of TVs in a randomly selected household Find the probability that a randomly selected family has more than 2 TVs This can be written as nd PXgt2 Math 1313 Class Notes 7 Section 81 Page 3 of5 De nition A histogram is a bar graph of a probability distribution Example 5 Draw a histogram from the probability distribution in Example 2 Example 6 Draw the histogram for the following probability distribution X l 3 5 7 PXX 03 035 02 015 Math 1313 Class Notes 7 Section 81 Page 4 of5 You ll be able to solve some problems using a probability distribution of a random variable Example 7 Consider the probability distribution of the random variable X x 0 2 4 6 8 PXx 12 21 47 15 05 Find a PX Z 4 b PXlt8 c P2ltXS6 d PXZO e PXSlO Math 1313 Class Notes 7 Section 81 Page 5 of5 Math 1313 Section 81 Distributions of Random Variables In Chapter 8 you will learn about random variables their probabilities distributions and three quantities that you can compute from a distribution of a random variable expected value variance and standard deviation You will also work some problems concerning two very common distributions of random variables the binomial distribution and the normal distribution The entire chapter relies on the concept of a random variable which we now de ne De nition A random variable is a function which assigns a number to each outcome of a chance experiment The domain of this function is the set of outcomes of the experiment and the range is the set of real numbers Example 1 An experiment consists of rolling a pair of fair dice and observing the numbers that fall uppermost on each die We can define a random variable X by assigning to each outcome of the experiment the number that is the absolute value of the difference between the two numbers rolled Notation We use capital letters printed or block letters hand written to denote random variables We usually use X first Then if the problem requires more than one random variable we use Y and then Z Example 2 Suppose a coin is tossed three times and we observe the whether heads or tails lands up on each toss and record the sequence of heads and tails Let the random variable X denote the number of tails observed in each outcome of the experiment a Find the value assigned to each outcome of the experiment by the random variable X Math 1313 Class Notes 7 Section 81 Page 1 of5

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