Question
In: Physics
Consider a series of 8 flips of a fair coin. Plot the entropy of each of...
Consider a series of 8 flips of a fair coin.
Plot the entropy of each of the 8 possible outcomes. Entropy is in J/K×1023J/K×1023
Entropy Number of heads012345678012345678910
Solutions
genius_generous answered 1 year agoRelated Solutions
Consider a series of 8 flips of a fair coin. Calculate the probabilities for obtaining 0-8...
Consider a series of 8
flips of a fair coin.
Calculate the
probabilities for obtaining 0-8 heads. We will consider each of
these nine outcomes to be macrostates of the system. Graph these
probabilities below.
ProbabilityNumber of
Heads0123456780.000.030.050.080.100.130.150.170.200.220.250.270.300.330.350.380.40
A fair coin is flipped six times. The outcomes of the coin flips form a palindrome...
A fair coin is flipped six times. The outcomes of the coin flips
form a palindrome if the sequence of T’s and H’s reads the same
forwards and backwards, e.g. THTTHT.
Let A denote the event that the first, second and fourth flips
are all ‘T’. Let Z denote the event that the six flips form a
palindrome.
(a) Is A independent of Z?
(b) Is A independent of Z?
(c) A fair coin flipped six times and a certain...
There is a fair coin and a biased coin that flips heads with probability 1/4.You randomly...
There is a fair coin and a biased coin that flips heads with
probability 1/4.You randomly pick one of the coins and flip it
until you get a heads. Let X be the number of flips you need.
Compute E[X] and Var[X]
Q. (a) Tegan is trying to decide if a coin is fair. She flips it 100...
Q.
(a) Tegan is trying to decide if a coin is fair. She flips it
100 times and gets 63 heads. Please explain why it might make sense
to view 63 heads as enough evidence to conclude the coin is
unfair.
(b) Leela is trying to decide if a coin is fair. She flips it
100 times and gets 63 heads. Please explain why it might NOT make
sense to view 63 heads as enough evidence to conclude the coin...
In a sequence of independent flips of a fair coin, let N denote the number of...
In a sequence of independent flips of a fair coin, let N denote
the number of flips until there is a run of three consecutive
heads. Find P(N ≤ 8). (Should write out transition matrix.)
Given that in 4 flips of a fair coin there are at least two "heads", what...
Given that in 4 flips of a fair coin there are at least two
"heads", what is the probability that there are two "tails"? There
are ten equally likely outcomes: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. You
randomly select one value, call it the initial value. Then, you
continue to randomly select values, call them follow-up selections,
until you come up with the initial value. What is the fewest number
of follow-up selections that insures that...
You roll two fair four-sided dies and then flip a fair coin. The number of flips...
You roll two fair four-sided dies and then flip a fair coin. The
number of flips is the total of the roll.
a. Find the expected value of the number of heads observed.
b. Find the variance of the number of heads observed.
Suppose 200 people are lined up side-by-side, each one holding a fair coin. Each person flips...
Suppose 200 people are lined up side-by-side, each one
holding a fair coin. Each person flips their coin 64 times; every
time it lands heads they step 1 meter forward, each time it lands
tails they step 1 meter backward. Use a normal approximation to
answer the following question: after everyone finishes their 64
steps, approximately how many people will be standing between 4 and
8 meters behind the starting line? (Round your answer to three
decimal places. Example: if...
Suppose 200 people are lined up side-by-side, each one holding a fair coin. Each person flips...
Suppose 200 people are lined up side-by-side, each one
holding a fair coin. Each person flips their coin 64 times; every
time it lands heads they step 1 meter forward, each time it lands
tails they step 1 meter backward. Use a normal approximation to
answer the following question: after everyone finishes their 64
steps, approximately how many people will be standing between 4 and
8 meters behind the starting line?
In a sequence of independent flips of a fair coin thwr comes up heads with probability...
In
a sequence of independent flips of a fair coin thwr comes up heads
with probability 0.6, what is the probability that there is a run
of three consecutive heads within the first 10 flips?
Show a Markov chain that counts the number of consecutive
heads attained.
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