CHAPTER 7 andom Variables Saluda County Schools7章随机变量S县学校.pptVIP

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CHAPTER 7 andom Variables Saluda County Schools7章随机变量S县学校.ppt

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CHAPTER 7 andom Variables Saluda County Schools7章随机变量S县学校

CHAPTER 5:Discrete Probability Distributions 5.1 Probability Distributions Random Variables A random variable is a variable whose value is a numerical outcome of a random phenomenon. let X = number of heads. if we get HHTH, X = 3 if we get TTTH, X = 1 What is the sample space for X? Random Variables they are variables because they keep changing they are random because we don’t know the next value the variable will assume. we DO know the overall pattern of the values assumed by a random variable over many repetitions. Random Variables A discrete random variable has a countable number of possible values. usually counts Random Variables A continuous random variable can take any value in an interval of the real number line. usually measurements ounces DISCRETE orCONTINUOUS? weight of a book number of chapters in a book number of defects in a square yard of fabric number of homeruns in a season weight of a boat-load of fish DISCRETE Random Variables We will use capital letters to represent discrete random variables usually X or Y corresponding lower case letters will represent values of the random variable. P(X = x) is the probability that the random variable X equals the value x. DISCRETE Random Variables the probability distribution of X lists the values and their probabilities. Value of X x1 x2 x3 … xk Probability p1 p2 p3 … pk Every pi is between 0 and 1. the sum of the p’s is 1. DISCRETE Random Variables Find the probability distribution for a gender for a family with three single births. Number of Boys 0 1 2 3 Probability Express P(at least two boys) in terms of X. find it. DISCRETE Random Variables Create a Probability Distribution for rolling a six sided die. DISCRETE Random Variables 25% of women cannot distinguish between the colors red and green. Find the probability distribution for 3 randomly chosen women. So, what is the probability that exactly two women will be colorblind? What is the probability that at least one will not be colorblind? DISCRETE