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Drstddengssigiment-Responses/submit?dep 18129319 E-Reserves (E Res) D faxzero.com D M Pom etoy :AppsBlackboard efax.com Assignment Scoring Your last submission is used for your score 1. 112 points I Previous PODStat5 7.E.006. My Not A person stands at the corner marked A of the square pictured below and tosses a coin. 9 ft If the coin lands heads up, the person moves one corner clockwise, to B. If the coin lands tails up, the person moves one person arrives back at A. Let y denote the number of coin tosses (a) What are possible values of y? O all positive odd integers all integers greater than 1 all integers greater than 2 o all positive integers greater than or equal to 4 O all positive even integers (b) Is y discrete or continuous? discrete O continuous You may need to use the appropriate table in Appendix A to answer this question EN D LL

Explanation / Answer

We observe that on one toss, the person is at B or D. From there, on second toss, that person is at A or C. From there, on third toss, that person is at B or D. From there, on fourth toss, that person is at A or C. This movement to same set of nodes on alternate tosses goes on forever. From this, we conclude that that person is at B or D on odd number of tosses. Also, that person is at A or C on even number of tosses.

(a)

y is the number of tosses to return to A. As per the rules, on odd number of coin tosses, it always lands at B or D, never at A. Also, for even number of coin tosses, it always lands at A or C. So, to return to A, it requires an even number of tosses.

So, the possible values of y are all positive even integers (option 5).

Option 1 is incorrect. For positive odd integers, it lands at B or D only.

Option 2 is also incorrect. All integers greater than 1 includes 3, 5, 7, ..., which we know always lands at B or D only.

Option 3 is incorrect for the same reason. All integers greater than 2 includes 3, 5, 7, ..., which we know always lands at B or D only.

Option 4 is incorrect for the same reason. All positive integers greater than or equal to 4 includes 5, 7, 9, ..., which we know always lands at B or D only.

(b)

y can take only even integer values. So, y is discrete.

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