# ch03 - -1 Introduction • Experiment • Random • Random...

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Unformatted text preview: -1 Introduction • Experiment • Random • Random experiment-1 Introduction-1 Introduction-1 Introduction-1 Introduction-2 Random Variables • In an experiment, a measurement is usually denoted by a variable such as X . • In a random experiment , a variable whose measured value can change (from one replicate of the experiment to another) is referred to as a random variable .-2 Random Variables-3 Probability • Used to quantify likelihood or chance • Used to represent risk or uncertainty in engineering applications • Can be interpreted as our degree of belief or relative frequency-3 Probability • Probability statements describe the likelihood that particular values occur. • The likelihood is quantified by assigning a number from the interval [0, 1] to the set of values (or a percentage from 0 to 100%). • Higher numbers indicate that the set of values is more likely.-3 Probability • A probability is usually expressed in terms of a random variable. • For the part length example, X denotes the part length and the probability statement can be written in either of the following forms • Both equations state that the probability that the random variable X assumes a value in [10.8, 11.2] is 0.25.-3 Probability Complement of an Event • Given a set E , the complement of E is the set of elements that are not in E . The complemen t is denoted as E ’ . Mutually Exclusive Events • The sets E 1 , E 2 ,..., E k are mutually exclusive if the intersection of any pair is empty. That is, each element is in one and only one of the sets E 1 , E 2 ,..., E k .-3 Probability Probability Properties-3 Probability Events • A measured value is not always obtained from an experiment. Sometimes, the result is only classified (into one of several possible categories). • These categories are often referred to as events . Illustrations • The current measurement might only be recorded as low, medium, or high ; a manufactured electronic component might be classified only as defective or not; and either a message is sent through a network or not. -4 Continuous Random Variables 3-4.1 Probability Density Function • The probability distribution or simply distribution of a random variable X is a description of the set of the probabilities associated with the possible values for X .-4 Continuous Random Variables 3-4.1 Probability Density Function-4 Continuous Random Variables 3-4.1 Probability Density Function-4 Continuous Random Variables 3-4.1 Probability Density Function-4 Continuous Random Variables 3-4.1 Probability Density Function-4 Continuous Random Variables...
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ch03 - -1 Introduction • Experiment • Random • Random...

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