AP Stat ch 7.1 - of the products The law of large numbers...

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AP Stat Chapter 7 7.1 Know about random variables and discrete random variables (have a countable number of possible values) The Probability must satisfy two requirements: - Every probability p i is a number between 0 and 1 - P i + P i + … P k = 1 Use probability histograms to picture the probability distribution of a discrete random variable The results of many trials are represented by a density curve of a uniform distribution. A continuous random variable is not countable. They are represented by a density curve. In random variables if x has a normal distribution then the standardized variable Z= is a standard normal random variable having the distribution N(1,0) 7.2 The mean of a random variable X is called the expected value ( or x ) Find the mean of X by multiplying each possible value by its probability, and then add all
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Unformatted text preview: of the products. The law of large numbers says as the number of observations increases, the mean of the observed values eventually reaches the mean of the population. The law of small numbers is just stating the opposite. Rules for means -If x is a random variable and a and b are fixed numbers then a +bx = a+b x-If X and Y are random variables then The variance of a discrete random variable x is each individual observation minus the mean of all of the observations squared times the probability of that point. You do this for each point and add them together. The standard deviation is the square root of the variance. Rules for variances -If X is a random variable and a and b are fixed numbers then 2 a+bx = b 2 2 x-If X and Y are independent random variables, then 2 xy = 2 x + 2 y...
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