Download Chapter 7 Notes

Chapter 7 Notes
7.1- Discrete and Continuous Random Variables
- Discrete random variable
o Has countable number of possible values
o Probabilities for each number (X) must be between 0 and 1
o The sum of all probabilities equals 1
o Probability histograms can be used to display this
- Continuous Random variable
o Takes all values in an interval of numbers
o Shown best by a density curve
o The probability of every individual outcome is 0
- Normal Distributions as Probability distributions
o N (mean, standard deviation)
o Standardized Z= X-mean/st. deviation
o In discrete just draw curve above histogram
7.2- Means and Variances of Random variables
- Mean of a Discrete random variable
o Multiply each possible value by its probability then add all
the products
o Mean often called expected value
o Mean(X) = x1p1+x2p2+…+xkpk
- Variance of a Discrete Random variable
o Variance = (x1-mean(x))^2*p1+ (x2-mean(x))^2*p2…
o Standard deviation is the square root of above
- Law of large numbers
o States that as SRS grows the observed mean will approach
the expected values for mean
o Intuition is bad at distinguishing random behavior from
systematic influences (possible at random- 9,9,9
o What constitutes a large number is different for each
situation
- Rules for Means
o If random variables a and b are fixed numbers
 Mean(a+bx) = a+b(meanx)
o If X and Y are random variable
 MeanX+Y= MeanX+MeanY
o Meanx+x+x=Mean3x
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- Rules for Variances
o If X is a random variable and a and b are fixed numbers
 Variance(a+bx)= b^2*Variance(x)
o If X and Y are independent
 Variance(X+Y) = Variance(x) + Variance(y)
 Variance(X-Y) = Variance(X) + Vaniance(Y)
o Always use variance to find standard deviation(square root
of above formulas)
- For fair game
o Expected value must equal zero