Question
In: Math
A. For a series of 1500 tosses, what is the natural logarithm of the total number...
A. For a series of 1500 tosses, what is the natural logarithm of the total number of microstates associated with 50% heads and 50% tails? (Note: Stirling’s approximation will be useful in performing these calculations).
B. How much less probable is the outcome that the coin will land 40% heads and 60% tails? (Note: Stirling’s approximation will be useful in performing these calculations).
Solutions
milcah answered 1 year agoRelated Solutions
In Java!! Problem 2 – Compute the sum of the series (19%) The natural logarithm of...
In Java!!
Problem 2 – Compute the sum of the series
(19%)
The natural logarithm of 2, ln(2), is an irrational number, and
can be calculated by using the following series:
1 - 1/2 + 1/3 - 1/4 + 1/5 - 1/6 + 1/7 - 1/8 + ... 1/n
The result is an approximation of ln(2). The result is more
accurate when the number n goes larger.
Compute the natural logarithm of 2, by adding up to n terms in...
In a series of 100 tosses of a token, the proportion of heads was found to...
In a series of 100 tosses of a token, the proportion of heads
was found to be 0.58. However, the margin of error for the estimate
on the proportion of heads in all tosses was too big. Suppose you
want an estimate that is in error by no more than 0.04 at the 95%
confidence level. (a) What is the minimum number of tosses required
to obtain this type of accuracy? Use the prior sample proportion in
your calculation. You...
2. Based on the data below: a) Plot the percentage of insects versus the natural logarithm...
2. Based on the data below:
a) Plot the percentage of insects versus the natural logarithm
of the dose.
b) Convert the data to probit variable, and plot the probit
versus the natural logarithm of the dose.
c) Determine the probit constants and the LC50. Please show all
calculations.
Dose of rotenone (mg/l)
Number of insects
Number affected (deaths)
9.1
60
47
7.0
73
51
6.4
49
32
5.3
35
20
4.4
54
18
2. Based on the data below: a) Plot the percentage of insects versus the natural logarithm...
2. Based on the data below:
a) Plot the percentage of insects versus the natural logarithm
of the dose.
b) Convert the data to probit variable, and plot the probit
versus the natural logarithm of the dose.
c) Determine the probit constants and the LC50. Please show all
calculations.
Dose of rotenone (mg/l)
Number of insects
Number affected (deaths)
9.1
60
47
7.0
73
51
6.4
49
32
5.3
35
20
4.4
54
18
A coin is tossed with P(heads) = p. a) What is the expected number of tosses...
A coin is tossed with P(heads) = p.
a) What is the expected number of tosses required to get n
heads?
b) Determine the variance of the number of tosses needed to get
the first head.
c) Determine the variance of the number of tosses needed to get
n heads.
A coin is tossed with P(heads) = p. a) What is the expected number of tosses...
A coin is tossed with P(heads) = p.
a) What is the expected number of tosses required to get n
heads?
b) Determine the variance of the number of tosses needed to get
the first head.
c) Determine the variance of the number of tosses needed to get
n heads.
Fair Coin? In a series of 100 tosses of a token, the proportion of heads was...
Fair Coin? In a series of 100 tosses of a
token, the proportion of heads was found to be 0.43. However, the
margin of error for the estimate on the proportion of heads in all
tosses was too big. Suppose you want an estimate that is in error
by no more than 0.05 at the 90% confidence level.
(a) What is the minimum number of tosses required to obtain this
type of accuracy? Use the prior sample proportion in your...
Fair Coin? In a series of 100 tosses of a token, the proportion of heads was...
Fair Coin? In a series of 100 tosses of a token, the
proportion of heads was found to be 0.43. However, the margin of
error for the estimate on the proportion of heads in all tosses was
too big. Suppose you want an estimate that is in error by no more
than 0.03 at the 95% confidence level.
(a) What is the minimum number of tosses required to obtain
this type of accuracy? Use the prior sample proportion in your...
Fair Coin? In a series of 100 tosses of a token, the proportion of heads was...
Fair Coin? In a series of 100 tosses of a
token, the proportion of heads was found to be 0.58. However, the
margin of error for the estimate on the proportion of heads in all
tosses was too big. Suppose you want an estimate that is in error
by no more than 0.05 at the 90% confidence level.
(a) What is the minimum number of tosses required to obtain this
type of accuracy? Use the prior sample proportion in your...
Fair Coin? In a series of 100 tosses of a token, the proportion of heads was...
Fair Coin? In a series of 100 tosses of a
token, the proportion of heads was found to be 0.58. However, the
margin of error for the estimate on the proportion of heads in all
tosses was too big. Suppose you want an estimate that is in error
by no more than 0.05 at the 90% confidence level.
(a) What is the minimum number of tosses required to obtain this
type of accuracy? Use the prior sample proportion in your...
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