PHYS 451 Quantum Mechanics I (Spring 2018) Homework #1, due Thursday Jan 25 in c

Question

PHYS 451 Quantum Mechanics I (Spring 2018) Homework #1, due Thursday Jan 25 in class Review of elementary probability In an experiment a die is thrown repeatedlv until a six turns up. When that happens the experiment is stopped. (a) What is the probability distribution function, p(k), that the experiment will last k throws? (b) Show that the total probability is p(k) = 1 (c) What is the most likely number of throws that will need to be done in this experiment? (d) What is the average number of throws. k), that will need to be done? (e) What is the standard deviation. ? Problem 1.11 in Griffiths Problem 1.16 in Griffiths

Explanation / Answer

a) p(k) = (5/6)^(k-1) * (1/6)
this is geometric distribution with p = 1/6
b) sum p(k) = 1/6 + 5/6 + (5/6)^2 + ...
= (1/6)/(1- 5/6)            {sum of GP = a/(1-r)}
= 1

c)

d) mean = 1/(1/6) = 6
e) sd = sqrt((1-p)/p^2) = sqrt((5/6)/(1/6)^2) = sqrt(30)

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