1. Explain why 60% of the time, the instructions in Fig. 3 return a 1 and 40% of the time, they return a 2. Type the instructions into your calculator, press the ENTER key 20 times, and count the number of 1s and 2s. Are there approximately twelve 1s and eight 2s?
Figure 3,

2. Explain why the instructions in Fig. 3 should not be replaced with this instruction:
(randInt (1,10) ‰¤ 6)1 + (randInt (1, 10) ‰¥7)2
Type this line into your calculator, and press the ENTER key several times to convince yourself that it does not always produce 1s and 2s.
In part 1, you pressed the ENTER key repeatedly and manually kept track of the outcomes. The TI-84 Plus can carry out the instructions many times, store the outcomes in a list, and analyze the list. The first instruction in Fig. 4 generates 100 random numbers between 1 and 10 and places them in the list L1. The second instruction of Fig. 4 converts each number in the list L1 to a row number by using the strategy [.6 .4] and places the 100 row choices into the list L3. Figure 6 uses the window settings shown in Fig. 5 to display the histogram for L3. We see that the second row was selected 44 times out of 100 times. This is close to the expected 40%.
Figure 4,

3. Explain in detail what is being calculated in Fig. 8?
Figure 8,

4. Suppose that a payoff matrix has three rows and that R's strategy is [.2 .5 .3]. Explain why Fig. 12 simulates the selection of a row by R. Type the instructions into your calculator, press the ENTER key 40 times, and count the number of 1s, 2s, and 3s. Are there approximately eight 1s, twenty 2s, and twelve 3s?

Transcribed Image Text:

NORMAL FLOAT AUTO REAL DEGREE CL randInt (1.10)+X: (XS6)1+(X2 7)2 randint (1,10)X: (XS6)1+(XE 7)2 randint (1,1ö)X: (XS6)1+(X2 7)2 1. NORMAL FLOAT AUTO REAL DEGREE MP randInt (1, 10, 100)+L1 (1 8 15 4 10 1 9 7 3 10 (L156)1+(L127)2+L3 (1 2.1 1 1 2 1 2 2 1 2.2