Please show all your work If you upload an image please make sure it is clear an

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Please show all your work

If you upload an image please make sure it is clear and your writing is legible.

Suppose you roll two (unweighted) 6-sided dice, and let x = the number of

Please show all your work If you upload an image please make sure it is clear and your writing is legible. Suppose you roll two (unweighted) 6-sided dice, and let x = the number of "2's" you get. (a) Show that the "parent" probability distribution P(x) for this system is: P(0) = 25/36 P(1) = 5/18 P(2) = 1/36 Note: it is not sufficient to simply use the Binomial distribution formula. Explain/show physically where each of the three probabilities comes from. (b) Find the (true) mean m and standard deviation sof x for this distribution. (c) Suppose you toss a pair of dice 100,000 times to measure an estimate of the mean. Make an estimate of how far you expect your estimate to deviate from the true mean.

Explanation / Answer

a) P(none) = 5/6 *5/6 = 25/36

P(1) = means 2 on one and anything else on other = 1/6 * 5/6 + 1/6*5/6 = 5/18

P(2) = 2 on both = 1/6*1/6 = 1/36

b) mean = 25/36*0 + 5/18*1 + 1/36*2=1/3

<x^2>=25/36*0^2 + 5/18*1^2 + 1/36*2^2=0.388

stdev = <x^2> - <x>^2 = 0.388 - 1/3^2=0.278

c) stdev of mean = stdev/sqrt(n) = 0.278/sqrt(100000)=8.79E-4

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