Simulations How To for Fathom

Transcription

1 Simulations How To for Fathom. Start by grabbing a collection box (the picture of a treasure box) and drop it on your screen. You can double click on the word collection to rename it. 2. Click on your collection box from step to HIGHLIGHT it. It should now have a blue square around it. Grab a case table (the picture of a table right next to the collection box icon from ) and drop it below the collection box. 3. Put a title like roll_ or roll in the top of the column where it says <new>. When you hit enter, a new <new> will appear. Type in roll 2 and so on to make as many columns as you have events in each trial. 4. Right click on the title of the column (attribute) to generate random numbers (see formula sheet) to represent ALL possible outcomes for each event. 5. Right click over your case table and select New Cases. Add new cases. Remember, we want MANY cases! But if you do more than, especially if you have several simulations in the same document, Fathom slows down a bit. When you hit enter, your case table should be full of numbers. Check to make sure these numbers are what you wanted. If not, go back in and check your random number formulas. 6. Create a check column. Title it something like number_of_sixes or number_of_rainy_days. You will most often want to use an IF statement here (see formula sheet). Once you hit enter, check the numbers in your check column to make sure that your formula is doing what you think it should be doing. 7. Grab a summary table and drop it next to your case table. Then drag and drop your check attribute into it. 8. Right click on the summary table, and add formula to count the number of trials that qualify as a success. You will most likely want to use a count statement here. To this formula, you can also add /columntotal to divide by the number of trials to give you the experimental probability. If you also x, you will get your experimental probability in percent. 9. Lastly, I suggest grabbing the graph icon, and dropping your check attribute into it. This gives you a visual representation of the various outcomes and their relative frequencies.

2 Important commands for Fathom No equal signs are necessary at the beginning of a formula in fathom. randominteger(,6) : generates random integers from to 6. Change the numbers and 6 to get the range you want. randompick( girl, boy ) or randompick( club, spade, diamond, heart)) or randompick( true, false ) : The random pick function will select from the list of elements in the bracket, with each element having the same probability of being chosen each time. Randompick(,,,) would return s and s, with s three times more likely than s. if(roll=2) This formula checks the attribute roll in the cell in the same row and if roll in that cell is equal to a 2, the contents of the cell containing this formula will be assigned the value. If roll is NOT equal to 2, the contents of the cell containing this formula will be assigned the value of. if(roll=2) if(roll2=2) if(roll3=2) if(roll4=2) As shown above, if statements can be stacked to check a set of attributes (a whole trial). If you simulated four rolls of a die, and you want to know the number of times a two was rolled, the above if statement will count the number of times the 2 was rolled in the given trial (or row). You can check for non-numerical stuff as well just remember to use your quotes, for example, if(child= girl )... Similarly, the following formula would count up all the rolls that have a value less than 3. if(roll<3) if(roll2<3) if(roll3<3) if(roll4<3) count(kicks=3) : This formula is usually used in a summary table, and will check all the cells in the whole column titled kicks and count up the number of 3s. Sum: In order to add up a set of attributes, you need to just add them: rollroll2roll3roll4. If you are interested in the total sum of a column, then in your summary table, enter the formula: sum(roll).

3 Simulations How To for Excel and Open Office. Put a title like roll, roll 2 and so on in the top row for as many columns as you have events in each trial. 2. Generate random numbers (see formula sheet) to represent ALL possible outcomes for each event. 3. Create one or more check columns. Sometimes you can check the random numbers for all the events in a trial with just one check. Or you may be more comfortable checking each event for success, then adding up the success. Either way, you will most likely want to use a COUNTIF statement here. 4. In a cell to the right of your work, write a statement like the number of successes is: 5. Then in the cell below, do another COUNTIF statement to tabulate the number of successes. 6. In another cell to the right of your work, below the one you created in step 4, write a statement like the experimental probability of (?whatever the question asks?) is: 7. then in the cell below, type =, then click on the cell you created in step 5, then / (divided by) and then the total number of trials you did.

4 Important commands for Excel and Open Office WHEN YOU USE OPEN OFFICE, REPLACE ALL THE COMMAS (, ) WITH SEMI-COLONS ( ; ) OR THE FORMULAS WON T WORK! =RANDBETWEEN(,6) : Generates a random integer between and 6. Replace the with the lowest number you want, and the 6 with the highest number you want. NOTE: in Open Office, use =RANDBETWEEN(;6) =INT(6*RAND()) : Generates a random integer between and 6. =INT(6*RAND()) : Generates a random integer between and 6. =CHOOSE((RANDBETWEEN(,3)),"true","false","chicken") : This statement selects a random number between and 3, then returns true if was selected, false if 2 was selected, and chicken if 3 was selected. Very useful!!! Especially if you replace true, false and chicken with other more useful type of words... Like: =CHOOSE((RANDBETWEEN (,4)),"club","diamond","heart","spade") =COUNTIF(A2:A22,3) : This function checks all the cells from A2 down to A22 and counts up the number of cells that contain a 3. NOTE: in Open Office, use =COUNTIF(A2:A22;3) =COUNTIF(A2:A22, >3 ) : This function checks all the cells from A2 down to A22 and counts up the number of cells that contain a number greater than 3. Anytime you want Excel to count up something that is not a number ( >3 or girl or yes ) you need to use quotes. NOTE: in Open Office, use =COUNTIF(A2:A22; >3 ) =SUM(A2:A22) : Sums all the values in the cells from A2 to A22. =IF(A2= girl, yes, no ) : This if-statement checks the cell A2, and if what s in cell A2 is girl, then it will return a yes to the cell that contains this function. If the cell does not contain girl, it will return the no. Again, if what Excel is checking for or returning is not a number, it needs quotes. NOTE: in Open Office, use =IF(A2= girl ; yes ; no ) =IF(AND(A2=,B2=,C2=,D2=2),"yes","no") This if-statement checks FOUR cells, A2, B2, C2, D2, and returns yes if all the values are true. This statement returns no if one or more of them are not true. NOTE: in Open Office, use =IF(AND(A2=;B2=;C2=;D2=2);"yes";"no")

5 How to Save Your Work. Log in to your Novell account. 2. Anytime you are asked to save a file, name it as instructed and save it to YOUR section of Novell. Do this early and save often. 3. Do not trust Novell. Always create a back up. You can do this by ing your work to yourself, by saving work on a USB drive, or by submitting temporary work to your teacher s handin folder. Lost work means lost time. No one can afford that! 4. When you are ready to send it to your teacher, have your folder open so you can see the icon of the file you want to send. 5. In a different window, open up your teacher s handin folder (Hudson) in the Docs section. 6. With both items (the handin folder and your file) visible, click on your file and drag it into the handin folder. 7. You should see it in the folder. It will disappear once your teacher has opened her folder. She will tell you if it has been received. Common mistakes: Trying to save as to the handin folder. You do not have that privilege. Forgetting to save the document in your own folder and then losing it completely. That s the worst! Forgetting to have both windows open at the same time. If you think (or know) that handing it in the first time didn t work, you must slightly rename your file. For ex. if it was supposed to be called JennyAssignment, resave it on your account as JennyGoodAssignment or JennyRealAssignment before you try and transfer the file a second time.