Please Answer :

From the Virtual Lab home page, go to the list of Applets. Under the Dice heading, select Dice Experiment. Famous Problems In 1693, Samuel Pepys asked Isaac Newton Whether it is more likely to get one ace in 6 rolls of a die or two aces in 12 rolls of a die. This problem is known as Pepys' problem and assumes that the dice are fair. . With n:6 dice, run the experiment 2000 times and find the binomial probability Answer of rolling Z = l ace on 6 dice. \"Distribution\" gives the classical probability. Here \"Data\" gives the empirical probability based on your simulation. Remember to change the random variable from the default Y : sum to Z : number of aces. P(one ace on 6 dice) Distribution Data Now with n:12, run the simulation 2000 times and find the binomial probability of rolling Z = 2 aces on 12 dice. Compare the results. P(two aces on 12 dice): 7777777 Distribution (Note that Pepys'probiem can be easily solved by hand using the binomial distribution probabilityformuia with n:6for 6diee and n : 12 for 12 dice. In either case, p : 1/6.) 5. So, what's the answer to Pepys' question? It is more likely to get one ace of six. 6. Calculate the following probabilities. An swe r H 9 re (Use the formula or the applet Distribution values.) P(3 aces with 13 dice) = __ E P(4 aces with 24 dice) = Note that the probabilities are declining at an exponential rate, For more information on Newton's response, see: https://www .wikiwand.com/eanewton %E2%80%93Pepys_problem Go to l-i"lt'11'.m01.Mahedtt/SFGI/ Click on Apps and find Bernoulli Trials. Thenfrom the applet (is: below, dick on Binomial Coin Experiment 1 . In the binomial coin experiment, vary a andp with the scrollbars, and note the shape and location ofthe probability density function. The empirical probabilities (red/Data) converge to the classical probabilities (blue/Distribution) for large n. For n = 10 and p = .4, find P(X=5) = _0.201_ For n = T" and p = .8, find P(X = 6) = _0.36?__ For n = 14 and p = .5, find the mean of the distribution _ 7.28 For n = 8 and p = .2, find the standard deviation of the distribution _1 .13 1_ For n = 10 and p = .8, run the simulation 1000 times and compare the empirical and classical probabilities for X = 8. Empirical: 0.309 Classical: 0.302 The binomial parameter p is called the \"shape\" parameter. Set n=10, and examine different values of p. Classify the shape as either symmetric or skewed. The shape of the distribution is ______ Skewed Right ________ when p is close to 0. The shape of the distribution is ______ Symmetrical _____ when p is close to 0.5. The shape of the distribution is _____ Skewed Left __________ when p is close to 1