Question
In: Advanced Math
Assume we are flipping 1000 fair coins. What can you say about the probability that you...
Assume we are flipping 1000 fair coins. What can you say about the probability that you will get at least 3/5 of them to be heads? Compare the 3 bounds (Markov, Chebyshev, Chernoff), and try plugging in some leargevalue of n to see how muchs they differ!
Solutions
Colby Messinger answered 1 year agoRelated Solutions
Consider flipping a fair coin 10 times. What is the probability that (a) you get exactly...
Consider flipping a fair coin 10 times. What is the probability
that
(a) you get exactly 7 heads?
(b) you get at least 4 heads?
(c) you get two more heads than tails?
Consider a statistical expirement of flipping a pair of fair coins simultaneously. Let X & Y...
Consider a statistical expirement of flipping a pair of fair
coins simultaneously. Let X & Y be the number heads in flipping
each coin.
Define a joint density function Z = XY. (I provided the answers
in bold but I need help understanding how it is solved. Thank you
in advance).
a) The number of possible distinct values of Z is:
2
b) The probability of Z = 0 is:
3/4
c) The mean of Z is: 1/4
d) The...
Consider independent trials of flipping fair coins (outcomes are heads or tails). Define the random variable...
Consider independent trials of flipping fair coins (outcomes are
heads or tails). Define the random variable T to be the first time
that two heads come up in a row (so, for the outcome HT HT HH... we
have T = 6).
(a) Compute P(T = i) for i = 1, 2, 3, 4, 5.
(b) Compute P(T = n) for n > 5.
You have 3 coins that look identical, but one is not a fair coin. The probability...
You have 3 coins that look identical, but one is not a fair
coin. The probability the unfair coin show heads when tossed is
3/4, the other two coins are fair and have probability 1/2 of
showing heads when tossed.
You pick one of three coins uniformly at random and toss it n
times, (where n is an arbitrary fixed positive integer).
Let Y be the number of times the coin shows heads. Let X be the
probability the coin...
In tossing three fair coins, what is the probability of getting at least two heads?
In tossing three fair coins, what is the probability of getting
at least two heads?
Two fair coins are flipped at the same time. 1) What is the probability of getting...
Two fair coins are flipped at the same time.
1) What is the probability of getting a match (same face on both
coins)? Answer for part 1 [The answer should be a number
rounded to five decimal places, don't use symbols such as
%]
2) What is the probability of getting at least two heads? Answer
for part 2 [The answer should be a number rounded to five
decimal places, don't use symbols such as %]
- Your friend claims he has a fair coin; that is, the probability of flipping heads...
- Your friend claims he has a fair coin; that is, the
probability of flipping heads or tails is equal to 0.5. You believe
the coin is weighted. Suppose a coin toss turns up 15 heads out of
20 trials. At α = 0.05, can we conclude that the coin is fair
(i.e., the probability of flipping heads is 0.5)? You may use the
traditional method or P-value method.
You have 100 coins, and 99 of them are fair (equal probability of heads or tails)....
You have 100 coins, and 99 of them are fair (equal probability
of heads or tails). One of them is weighted and has a 90%
probability of landing on heads. You randomly choose one of the 100
coins. Find the probability that it is a weighted coin, under the
following scenarios: (Hint: if your calculator can’t compute 100!,
R can, just type factorial(100))
(a) You flip it 10 times and lands on heads 10 times (b) You
flip it 10...
A box contains 5 fair coins, 4 coins that land heads with probability 1/3 , and...
A box contains 5 fair coins, 4 coins that land heads with
probability 1/3 , and 1 coin that lands heads with probability 1/4
. A coin is taken from the box at random and flipped repeatedly
until it has landed heads three times. Let X be the number of times
that the coin is flipped and Y be the probability that the coin
lands heads.
(a) Find the random variables E(X|Y ) and var(X|Y ) in terms of
Y...
A box contains 5 fair coins, 4 coins that land heads with probability 1/3 , and...
A box contains 5 fair coins, 4 coins that land heads with
probability 1/3 , and 1 coin that lands heads with probability 1/4
. A coin is taken from the box at random and flipped repeatedly
until it has landed heads three times. Let X be the number of times
that the coin is flipped and Y be the probability that the coin
lands heads.
(a) Find the random variables E(X|Y ) and var(X|Y ) in terms of
Y...
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