Question
In: Statistics and Probability
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 .
(b) Compute E(X).
(c) Compute var(X).
Solutions
orchestra answered 1 year agoRelated Solutions
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...
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]
A box contains three fair coins and one biased coin. For the biased coin, the probability...
A box contains three fair coins and one biased coin. For the
biased coin, the probability that any flip will result in a head is
1/3. Al draws two coins from the box, flips each of them once,
observes an outcome of one head and one tail and returns the coins
to the box. Bo then draws one coin from the box and flips it. The
result is a tail. Determine the probability that neither Al nor Bo
removed the...
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?
4 fair coins are tossed. Let X be the number of heads and Y be the...
4 fair coins are tossed. Let X be the number of heads and Y be
the number of tails. Find Var(X-Y)
Solution: 3.5
Why?
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 4 quarters, 3 dimes, and 2 nickels. a. Two coins are selected at...
A box contains 4 quarters, 3 dimes, and 2 nickels.
a. Two coins are selected at random without replacement one at a
time. Compute the probability that the first coin is a dime and the
second is a nickel.
b. Three coins are selected at random with replacement. Compute
the probability that at least one of them is a nickel.
c. Construct a probability distribution of the number of
quarters selected for a procedure of selecting three coins without
replacement....
A box contains 4 quarters, 3 dimes, and 2 nickels. a. Two coins are selected at...
A box contains 4 quarters, 3 dimes, and 2 nickels.
a. Two coins are selected at random without replacement one at a
time. Compute the probability that the first coin is a dime and the
second is a nickel.
b. Three coins are selected at random with replacement. Compute
the probability that at least one of them is a nickel.
c. Construct a probability distribution of the number of
quarters selected for a procedure of selecting three coins without
replacement....
Three fair coins are tossed simultaneously 10 times. Find the probability that "2 heads and one...
Three fair coins are tossed simultaneously 10 times. Find the
probability that "2 heads and one tail" will show up (a) at least
once and (b) at most once.
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