PLEASE HELP For this exercise four coins are tossed 32 times and the number of h

Question

PLEASE HELP

For this exercise four coins are tossed 32 times and the number of heads are recorded for each toss. Each toss falls into one of the following macroscopic states; 0 heads. 1 heads. 2 heads. 3 heads and 4 heads Suppose the 32 tosses result in the following outcome: 2.3 1.2.1.2.3.2.1.1.4.3.3.3.2.3, 2.3.2.3.11 3.1.4.2,3.3.2.2.2 and 3. Your task is to count the number of times when 1 heads. 2 heads,.... appears, and to calculate the measured and expected distribution functions. To calculate the measured distribution function if nj is the number of counts for jth heads for N trials, then the experimental distribution function is fj = n1/N. For example, the number of counts with zero heads is 0 giving f0 = 0/32 = 0. The expected distribution for such an experiment follows a binomial distribution function and is given by f st j = C!/(C-xj)!xj!22CC where C is the total number of coins, Xj is the number of heads Thus for the case of 0 heads, f0 = 4!/(4-0)!0!24 = 1/16 = 0.0625. (Learn more about expected distribution functions.) Using Equations [1] and [2] calculate the average number of heads and the standard deviation and enter the values below. Do this for the measured and the expected cases.

Explanation / Answer

measured values:

average = (7*1+11*2+12*3+2*4)/32 = 2.28

standard deviation = sqrt(sigma{(xj - <x>)^2 fj})

standard deviation = sqrt((1-2.28)^2*7 + (2-2.28)^2*11 + (3-2.28)^2*12 +(4-2.28)^2*2)

standard deviation = sqrt(11.4912 + 0.8701 + 6.1992 + 5.908)

standard deviation = 4.95

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