Probability experimenting Coin&Die https://davidwills.us/math103/coin_die.html Coin flips 100 automatically. 3 times, (Clearing each time) %heads:______ %tails:_______ |%difference|:_____ %heads:______ %tails:_______ |%difference|:_____ %heads:______ %tails:_______ |%difference|:_____ 1000 automatically. 3 times, (Clearing each time) %heads:______ %tails:_______ |%difference|:_____ %heads:______ %tails:_______ |%difference|:_____ %heads:______ %tails:_______ |%difference|:_____ 10000 automatically. 3 times, (Clearing each time) Display flips? No (maybe speeds up) %heads:______ %tails:_______ |%difference|:_____ %heads:______ %tails:_______ |%difference|:_____ %heads:______ %tails:_______ |%difference|:_____ The Law of Large Numbers: the more times a probability experiment (e.g. a coin flip) occurs, the more the actual number of occurences approaches the expected theoretical number (e.g. half). ******************************************************************* Die toss Each number has a 1/6 = .166666666 chance of being top. 100 %1______ %2______ %3______ %4______ %5______ %6______ 1000 %1______ %2______ %3______ %4______ %5______ %6______ 10000 don't display %1______ %2______ %3______ %4______ %5______ %6______ 100000 don't display %1______ %2______ %3______ %4______ %5______ %6______ ******************************************************************* Sum of two dice. + 1 2 3 4 5 6 1 2 3 4 5 6 Frequency distribution table. incl. relative frequency Sum Frequency Rel freq 2 3 4 5 6 7 8 9 10 11 12 Do the frequency and relative frequency columns look symmetric?:___ What sum is the mode?:___ ******************************************************************* Dice rolls #dice: 2 #rolls: 100 #rolls: 1000 #rolls: 10000 Relative frequencies getting closer and closer to the theoretical probabilities. Do the frequency and relative frequency columns look symmetric?:___ What sum is the mode?:___ Rotating 90 degrees these columns look histogram-ish. Do 1000 rolls. Sum=______ divided by 1000=_______ the average sum of the 1000 rolls. Copy and paste the 1000 rolls into freq dist, histogram, stats *** https://davidwills.us/math103/freq_histogram.html n=____ mean=______ median=______ mode=_______ SD=_______ Sketch the histogram of X from 0 to 13, class width of 1: This distribution sure looks like a ___________ distribution.