Names: Flip me Off Coin Flipping Exercise is lablet explores some statistics tha

Question

Names: Flip me Off Coin Flipping Exercise is lablet explores some statistics that will lead into our discussion of entropy. Your group will be given veral pennies, which you will flip several times. Sometimes you will lip two pennies, sometimes 4, r 16. On each flip you will count the total number of heads and record how often that number of heads ccurs 1. Flip 2 pennies 32 times. (Several pairs of people can do this.) Record results below. Number of heads Number of times To figure out the expected value, remember that 2 pennies can fall in any of 2 -4 ways. Figure out how many of those ways would give you 2 heads, I head, and zero heads; this gives you the probability of each outcome. For example, there is only one way to get 2 heads, so the probability of 2 heads is Hence you expect that a quarter of your 32 trials (8) should give 2 heads To find the expected values for larger numbers of pennies, note that N pennies can fall in 2" ways, and the number of ways you can choose m heads out of N pennies ismiN-m Here the notation N1 represents N factorial-N x (N-1) × (N-2) x 2 × 1· 01 is defined to be equal to 1 N! 2. Flip 4 pennies 64 times and record your results below Number of times ted

Explanation / Answer

a) Expected value is given by SUm of P(x)*Xi where Xi is the number of heads.

a) E(x) = 8*2+16*1+8*0 / 32 = 1 head.

This is logical since 2 pennies should give 1 head and 1 tail in each trial max number of times.

b) E(x) =[ 4*4+16*3+24*2+16*1+4*0]/64=2

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