Outline The Normal PDF and CDF Lab Assignment 3 Lab3 Continuous Distributions M George Akritas M George Akritas Lab3 Continuous Distributions Outline The Normal PDF and CDF Lab Assignment 3 The Normal PDF and CDF Lab Assignment 3 Due Date M George Akritas Lab3 Continuous Distributions Outline The Normal PDF and CDF Lab Assignment 3 Plotting and comparing 1 Plotting the standard normal pdf and cdf 1 1 Make a grid of points on the x axis x seq 4 4 0 01 1 2 Calculate the standard normal pdf and cdf for each point in the grid yd dnorm x yp pnorm x comma within means hit return 1 3 Plot the pdf and cdf plot x yd type l plot x yp type l 1 4 Superimpose the two plots plot x yd type l lines x yp type l 2 Superimposing three normal PDFs plot x dnorm x 0 0 5 type l col blue lines x dnorm x type l col red lines x dnorm x 0 2 type l col black M George Akritas Lab3 Continuous Distributions Outline The Normal PDF and CDF Lab Assignment 3 Marking and shading 1 Plot the standard normal PDF and mark the 90th percentile plot x dnorm x type l lines qnorm 0 9 dnorm qnorm 0 9 type h col red 2 Mark the 90th percentile on the CDF plot plot x pnorm x type l lines qnorm 0 9 pnorm qnorm 0 9 type h col red 3 Shade the area under the N 0 1 pdf to the right of the 90th percentile x1 seq qnorm 0 9 4 0 01 y1 dnorm x1 plot x dnorm x type l lines x1 y1 type h col red M George Akritas Lab3 Continuous Distributions Outline The Normal PDF and CDF Lab Assignment 3 Due Date Properties of the Normal 1 Using the R commands pnorm x for x and 1 pnorm x for 1 x and three positive x values of your choice it is best if your numbers are not greater than 3 verify that x 1 x holds for any x 0 I I Report the three x values that you chose and the corresponding x and 1 x values Give an explanation of x 1 x using the geometrical interpretation of these quantities as areas under the standard normal pdf A non geometrical explanation is as follows If Z N 0 1 then Z N 0 1 Thus for any x 0 x P Z x P Z x P Z x 1 x M George Akritas Lab3 Continuous Distributions Outline The Normal PDF and CDF Lab Assignment 3 Due Date 2 Using the R commands pnorm x for P X x where X N 2 and pnorm x for x and three sets of x values of your choice pick any number for any positive number for and pick a value for x such that 3 x 3 and do this three times verify that x P X x I Report the three sets of x values that you chose and the corresponding P X x and x values M George Akritas Lab3 Continuous Distributions Outline The Normal PDF and CDF Lab Assignment 3 Due Date 3 Using the R command qnorm 1 for the 100 1 th percentile x of X N 2 verify that x1 x by computing the two sides of the above equation for three different values of between 0 and 0 5 and any pair of values I Report the pair of values you chose the three different values of you chose and the corresponding values of the two sides of the equation M George Akritas Lab3 Continuous Distributions Outline The Normal PDF and CDF Lab Assignment 3 Due Date Email your answers to Ms Lauren Kraus by Friday Oct 7th M George Akritas Lab3 Continuous Distributions Outline The Normal PDF and CDF Lab Assignment 3 Due Date I Go to previous lab http www stat psu edu mga 401 course info b lab Ch2 pdf I Go to next lab http www stat psu edu mga 401 course info b lab Ch4a pdf I Go to the Stat 401 home page http www stat psu edu mga 401 course info I http www stat psu edu mga http www google com I M George Akritas Lab3 Continuous Distributions