# CH 4 - Probability:TheStudyof Randomness RandomVariables...

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Probability: The Study of  Randomness  随随随 Random Variables

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Objectives Random variables 任任任任任任任任任 Discrete random variables 随随随随随随随随 Continuous random variables Normal probability distributions 随随随随随随 Mean of a random variable Law of large numbers Variance of a random variable 随随随随随随随 Rules for means and variances
A phenomenon is random if individual outcomes are uncertain, but there is nonetheless 随随随随随随随 a regular distribution of outcomes in a large number of repetitions 随随随随随 . Randomness and probability 随随随随随随 The probability of any outcome of a random phenomenon can be defined as the proportion of times the outcome would occur in a very long series of repetitions.

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Coin toss The result of any single coin toss 随随随 is random. But the result over many tosses is predictable 随随随随 , as long as the trials 随随 are independent (i.e., the outcome of a new coin flip is not influenced by the result of the previous flip). The result of any single coin toss 随随随 is random. But the result over many tosses is predictable 随随随随 , as long as the trials 随随 are independent (i.e., the outcome of a new coin flip is not influenced by the result of the previous flip). First series of tosses Second series The probability of heads is 0.5 = the proportion of times you get heads in many repeated trials.
Discrete random variables 随随随随随随随 A random variable is a variable whose value is a numerical outcome of a random phenomenon. A basketball player shoots three free throws. We define the random variable X as the number of baskets successfully made. A discrete random variable X has a finite number of possible values ( 随随随随 ) A basketball player shoots three free throws. The number of baskets successfully made is a discrete random variable ( X ). X can only take the values 0, 1, 2, or 3.

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The probability distribution of a random variable X lists the values and their probabilities: The probabilities p i must add up to 1. 随随随 1 A basketball player shoots three free throws. The random variable X is the number of baskets successfully made.
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