5) We want to explore the effect of parameters on a binomial distribution (this is a bit similar to last week's assignment). Start up R/RStudio a) First we'll do our coin example from lecture but use 12 tosses instead of 10. Let's calculate those probabilities and plot a graph so we know what our "distribution" looks like: In the script window or on the command line do the following: y Homework # 5: (Do not use R for problems 1 - 4) 1) Find the following probabilities: a) Pr{Z (d) Can you understand how important the parameters of a distribution are? What do the parameters of a distribution tell us about the distribution? (f) At this point your graph should have four curves plotted on top of each other in your final graph. Copy this graph and paste it into a word processor or whatever you want to use so that you can print a copy. Optional: if you want to make your graph look even nicer, you can add the following: legend (-4.5,0.39, c("mean = 0, sd = 1","mean = 1, sd = 1", "mean = 0, sd = 2", "mean = 1.5, sd = 1.7"), col = c("red","blue","green","purple"), Ity = c(1,1,1,1)) The legend command can get pretty complicated. Here's a breakdown of what's going on: The first two numbers (-4.5, 0.39) give the x and y coordinates of the top left corner of the legend box. These coordinates are the same ones used in the plot. The first "c(...)" contains the actual labels for the legend. In this case we want to combine four "labels", one for each line in our plot ("c" means combine or concatenate). The "col = c(...)" part gives the four colors we want to use (we need to make sure they match the ones used in the plot and are in the same order as the first c(...) which has the labels). Finally, we need to tell R what we used for plotting - we used lines, and "Ity(...)" tells R to draw lines of the appropriate colors in our legend. The ones (1's) inside the Ity command tell R to draw simple lines (R can draw many different kinds of lines - try using 2's or 3's here and you'll see what this means). ******************************* Copying and pasting graphs from R: See instructions from the previous set of homework. ***** ************* Problems are due in recitation the week of February 27th. 6) Now let's try a normal distribution. The first plot will be easy, but the second will be more difficult to do, so follow the instructions carefully. First we'll plot a standard normal, then we'll see what happens if you change the parameters. x