Question
In: Math
The coins (by magic) always land on the same side (both heads or both tails). Suppose...
The coins (by magic) always land on the same side (both heads or both tails). Suppose you flip a penny and a dime. Let X be the result of flipping the penny where we assign the value of Heads to be 2 and the value of Tails to be 1, and let Y be the result of flipping the dime where we assign the value of Heads to be 4 and Tails to be 3. (So, for example, X(heads)=2.) Find E[X], E[Y], E[X+Y] andE[XY]. Compute Var(X+Y) and Var(XY).
Solutions
milcah answered 1 month agoRelated Solutions
A weighted coin has a probability of 0.6 to land on “tails” and will always land...
A weighted coin has a probability of 0.6 to land on “tails” and
will always land on either “heads” or “tails.” Which of the
following statements is false?
If 100 people were to flip the coin once each, approximately 60%
of them will observe “tails.”
After flipping the coin 5 times, the observed results will be 3
“tails” and 2 “heads.”
The probability of flipping the coin once and observing “heads”
is 0.4.
Each person who flips the coin has...
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...
Problem 4) Five coins are flipped. The first four coins will land on heads with probability...
Problem 4) Five coins are flipped. The first four coins will
land on heads with probability 1/4. The fifth coin is a fair coin.
Assume that the results of the flips are independent. Let X be the
total number of heads that result.
(hint: Condition on the last flip).
a) Find P(X=2)
b) Determine E[X]
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.
One fair coin and two unfair coins where heads is 5 times as likely as tails...
One fair coin and two unfair coins where heads is 5 times as
likely as tails are put into a bag. One coin is drawn at random and
then flipped twice. If at least one of the flips was tails, what is
the probability an unfair coin was flipped?
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...
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...
Two coins are tossed at the same time. Let random variable be the number of heads...
Two coins are tossed at the same time. Let random variable be
the number of heads showing.
a) Construct a probability distribution for
b) Find the expected value of the number of heads.
is the pka of a histidine side chain always the same as that of the free...
is the pka of a histidine side chain always the same as that of
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how do titration curves differ between non ionizable and
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Biochemistry
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