Lecture 5.pdf

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Classical Studies
Douglas Frayne

Reminder: - Quiz:open notebook and textbook,and non-programmable calculator Multiple choice or true/false Density Curve - area underneath is 1 - area underneath between two certain points is the proportion of values of the variables that are between those two points - denote by X some variable,what does it mean to say X has density curve/ distribution given by some curve? - Recall: - if we have a data set,we can calculate sample mean,sample median,sample standard deviation,sample IQR - also attached to a density curve are numbers describing center and spread - stick density curve inside this techniques of calculus box which finds the distribution mean denoted by and sigma for standard deviation - distribution mean describes the center of density curve - distribution standard deviation describes the spread of density curve Normal Density Curves - a special class of density curves - formula:the height of a normal density curve is given by the following formula: (get in the book) - note:there are two parameters in this formula,sigma can only be positive real numbers and u can be any real number - looks like this: - the height of this curve for any particular x is the formula - for the mean it will u and for the standard deviation it will sigma - note:when a variable X has normal density curve we write X ~ N(u,sigma).~ means distributed - note:when u = 0 and sigma =1 distribution is called the standard normal density curve - u is the balancing point of the density curve - sigma,the proportion of the values that fall within 1 standard deviation (u - sigma) is .68,2 standard dev
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