Question: D E F AL B Coin-Flipping Game 1 2 3 4 S 6 7 Required Difference Cash at End of Game Summary of Game Number

D E F AL B Coin-Flipping Game 1 2 3 4 S 6 7

D E F AL B Coin-Flipping Game 1 2 3 4 S 6 7 Required Difference Cash at End of Game Summary of Game Number of Flips 11 Winnings -$3 8 9 Total Heads Stop? 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 Total Tails 0 1 2 3 3 1 1 1 2 3 Flip 1 2 3 4 S 6 7 8 9 10 11 12 13 14 Random Number 0.3039 0.7914 0.8543 0.6902 0.3004 0,0383 0.3883 0.6052 0.2231 0.4250 0.3729 0.7983 0.2340 0.0082 Result Heads Tails Tails Tails Heads Heads Heads Tails Heads Heads Heads Tails Heads Heads 4 4 5 6 7 7 8 9 3 3 4 4 4 4 5 5 5 Stop NA NA NA 12.4. The weather can be considered a stochastic system, because it evolves in a probabilistic manner from one day to the next. Suppose for a certain location that this probabilistic evolution satisfies the following description: The probability of rain tomorrow is 0.6 if it is raining today. The probability of its being clear (no rain) tomorrow is 0.8 if it is clear today. a. Use the random numbers in cells C17:C26 of Figure 12.1Q to simulate the evolution of the weather for 10 days, beginning the day after a clear day. E b. Now use a computer with the random numbers generated by Excel to perform the simulation requested in part a on a spreadsheet. FIGURE 12.1 A spreadsheet model for a computer simulation of the coin-flipping game (Example 1). AL Coin-Flipping Game B D F 1 2 3 Required Difference Cash at End of Game 3 $8 Number of Flips Winnings Summary of Game 11 -S2 Total Tails Stop D Result Heads Tails Tails 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 57 58 59 60 Flip 1 2 3 4 $ 6 7 8 9 Total Heads 1 1 1 1 2 ! 2 3 3 3 Heads Heads Heads 4 This Random Number 0.3039 0.7914 0.8543 0.6902 0,3004 0,0383 DINO 0.6052 0.2231 0.4250 03729 0,7983 0.2340 0.0082 0.7539 0.2989 0.6427 0.2824 02124 0.6420 3 4 4 4 4 10 11 12 13 14 45 46 47 48 49 SO Heads Heads Heads This Heads Heads This Heads This Heads Heads This 4 5 6 7 7 8 9 26 27 27 28 29 29 5 5 5 19 19 20 20 20 21 Stop NA NA NA NA NA NA NA NA NA 62 Range Name Cells CashAtEndOfGame D4 Flip BI):362 NumberOnFlips D7 Random Number C13:062 Required Difference D3 Result D13-062 Stop? G13:662 TotalHeads E13 E62 Total Tails F13:F62 Winnings DS C. 6 7 D Summary of Game Number of Flips -COUNTBLANK/Stop!)+1 Winnings -CashAtEndOfGame-NumberOfFlips I! Random 12 Number 13 -RAND) 14 -RAND) 15 -RAND) 16 17 D E Total Result Heads IF(Random Number0.5. "Heads", "Tails") IF(Results"Heads".1.0) - IF(Random Number0.5. "Heads", "Tails")-E13 IF(Results-"Heads"1.0) - IF(Random Numbers0.5. "Heads", "Tails")-E14+IF(Results-"Heads.1.0) F Total Tails -FlipTotalHeads -FlipTotalHeads - Flip-TotalHeads 12 Stop? 13 14 15 IF(ABS Total Heads Total Tils)-Required Difference,"Stop") 16 IF(GIS-IF(ABS(TotalHeads Totalais-Required Difference,"Stop".). "NA") 17-IF(G16"IF(ABS(Total Heads Total Tails)-Required Difference,"Stop"."). "NA) 18 19 D E F AL B Coin-Flipping Game 1 2 3 4 S 6 7 Required Difference Cash at End of Game Summary of Game Number of Flips 11 Winnings -$3 8 9 Total Heads Stop? 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 Total Tails 0 1 2 3 3 1 1 1 2 3 Flip 1 2 3 4 S 6 7 8 9 10 11 12 13 14 Random Number 0.3039 0.7914 0.8543 0.6902 0.3004 0,0383 0.3883 0.6052 0.2231 0.4250 0.3729 0.7983 0.2340 0.0082 Result Heads Tails Tails Tails Heads Heads Heads Tails Heads Heads Heads Tails Heads Heads 4 4 5 6 7 7 8 9 3 3 4 4 4 4 5 5 5 Stop NA NA NA 12.4. The weather can be considered a stochastic system, because it evolves in a probabilistic manner from one day to the next. Suppose for a certain location that this probabilistic evolution satisfies the following description: The probability of rain tomorrow is 0.6 if it is raining today. The probability of its being clear (no rain) tomorrow is 0.8 if it is clear today. a. Use the random numbers in cells C17:C26 of Figure 12.1Q to simulate the evolution of the weather for 10 days, beginning the day after a clear day. E b. Now use a computer with the random numbers generated by Excel to perform the simulation requested in part a on a spreadsheet. FIGURE 12.1 A spreadsheet model for a computer simulation of the coin-flipping game (Example 1). AL Coin-Flipping Game B D F 1 2 3 Required Difference Cash at End of Game 3 $8 Number of Flips Winnings Summary of Game 11 -S2 Total Tails Stop D Result Heads Tails Tails 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 57 58 59 60 Flip 1 2 3 4 $ 6 7 8 9 Total Heads 1 1 1 1 2 ! 2 3 3 3 Heads Heads Heads 4 This Random Number 0.3039 0.7914 0.8543 0.6902 0,3004 0,0383 DINO 0.6052 0.2231 0.4250 03729 0,7983 0.2340 0.0082 0.7539 0.2989 0.6427 0.2824 02124 0.6420 3 4 4 4 4 10 11 12 13 14 45 46 47 48 49 SO Heads Heads Heads This Heads Heads This Heads This Heads Heads This 4 5 6 7 7 8 9 26 27 27 28 29 29 5 5 5 19 19 20 20 20 21 Stop NA NA NA NA NA NA NA NA NA 62 Range Name Cells CashAtEndOfGame D4 Flip BI):362 NumberOnFlips D7 Random Number C13:062 Required Difference D3 Result D13-062 Stop? G13:662 TotalHeads E13 E62 Total Tails F13:F62 Winnings DS C. 6 7 D Summary of Game Number of Flips -COUNTBLANK/Stop!)+1 Winnings -CashAtEndOfGame-NumberOfFlips I! Random 12 Number 13 -RAND) 14 -RAND) 15 -RAND) 16 17 D E Total Result Heads IF(Random Number0.5. "Heads", "Tails") IF(Results"Heads".1.0) - IF(Random Number0.5. "Heads", "Tails")-E13 IF(Results-"Heads"1.0) - IF(Random Numbers0.5. "Heads", "Tails")-E14+IF(Results-"Heads.1.0) F Total Tails -FlipTotalHeads -FlipTotalHeads - Flip-TotalHeads 12 Stop? 13 14 15 IF(ABS Total Heads Total Tils)-Required Difference,"Stop") 16 IF(GIS-IF(ABS(TotalHeads Totalais-Required Difference,"Stop".). "NA") 17-IF(G16"IF(ABS(Total Heads Total Tails)-Required Difference,"Stop"."). "NA) 18 19

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