6.6.1 Draw
histograms describing the probabilities of the outcomes of four
experiments to count the number of mutants in a bacterial cultural. ... Experiment a.
Get solution
6.6.2 Draw
histograms describing the probabilities of the outcomes of four
experiments to count the number of mutants in a bacterial cultural. ... Experiment b.
Get solution
6.6.3 Draw
histograms describing the probabilities of the outcomes of four
experiments to count the number of mutants in a bacterial cultural. ... Experiment c.
Get solution
6.6.4 Draw
histograms describing the probabilities of the outcomes of four
experiments to count the number of mutants in a bacterial cultural. ... Experiment d.
Get solution
6.6.5
Find and sketch the cumulative distribution associated with the
histogram from the earlier problem. The histogram in Exercise 1.
Reference Exercise 1. Draw
histograms describing the probabilities of the outcomes of four
experiments to count the number of mutants in a bacterial cultural.
... Experiment a.
Get solution
6.6.7
Find and sketch the cumulative distribution associated with the
histogram from the earlier problem. The histogram in Exercise 3.
Reference Exercise 3. Draw
histograms describing the probabilities of the outcomes of four
experiments to count the number of mutants in a bacterial cultural.
... Experiment c.
Get solution
6.6.7
Find and sketch the cumulative distribution associated with the
histogram from the earlier problem. The histogram in Exercise 3.
Reference Exercise 3. Draw
histograms describing the probabilities of the outcomes of four
experiments to count the number of mutants in a bacterial cultural.
... Experiment c.
Get solution
6.6.8
Find and sketch the cumulative distribution associated with the
histogram from the earlier problem. The histogram in Exercise 4.
Reference Exercise 4. Draw
histograms describing the probabilities of the outcomes of four
experiments to count the number of mutants in a bacterial cultural.
... Experiment d.
Get solution
6.6.9 On each histogram, find the most and least likely simple events. Is the histogram symmetric? ...
Get solution
6.6.10 On each histogram, find the most and least likely simple events. Is the histogram symmetric? ...
Get solution
6.6.11 On each histogram, find the most and least likely simple events. Is the histogram symmetric? ...
Get solution
6.6.12 On each histogram, find the most and least likely simple events. Is the histogram symmetric? ...
Get solution
6.6.13 Using the histogram indicated, estimate the probabilities of the following events.
a. The measurement is equal to 7.
b. The measurement is less than or equal to 4.
c.
The measurement is greater than 4. The histogram in Exercise
9.Exercise 9 On each histogram, find the most and least likely simple
events. Is the histogram symmetric? ...
Get solution
6.6.14 Using the histogram indicated, estimate the probabilities of the following events.
a. The measurement is equal to 7.
b. The measurement is less than or equal to 4.
c.
The measurement is greater than 4. The histogram in Exercise
10.Exercise 10 On each histogram, find the most and least likely simple
events. Is the histogram symmetric? ...
Get solution
6.6.15 Using the histogram indicated, estimate the probabilities of the following events.
a. The measurement is equal to 7.
b. The measurement is less than or equal to 4.
c.
The measurement is greater than 4. The histogram in Exercise
11.Reference On each histogram, find the most and least likely simple
events. Is the histogram symmetric? ...
Get solution
6.6.16 Using the histogram indicated, estimate the probabilities of the following events.
a. The measurement is equal to 7.
b. The measurement is less than or equal to 4.
c.
The measurement is greater than 4. The histogram in Exercise
12.Exercise 12. On each histogram, find the most and least likely
simple events. Is the histogram symmetric? ...
Get solution
6.6.17 Check that the area under the curve is exactly 1.
a. Check that the area under the curve is exactly 1.
b. Sketch a graph.
c. Indicate the maximum of the p.d.f., and explain why you are not worried that it is sometimes greater than 1. The p.d.
f. is f (x)=2x for 0≤ x ≤1.
Get solution
6.6.18 Check that the area under the curve is exactly 1.
a. Check that the area under the curve is exactly 1.
b. Sketch a graph.
c. Indicate the maximum of the p.d.f., and explain why you are not worried that it is sometimes greater than 1. ...
Get solution
6.6.19 Check that the area under the curve is exactly 1.
a. Check that the area under the curve is exactly 1.
b. Sketch a graph.
c. Indicate the maximum of the p.d.f., and explain why you are not worried that it is sometimes greater than 1. ...
Get solution
6.6.20 Check that the area under the curve is exactly 1.
a. Check that the area under the curve is exactly 1.
b. Sketch a graph.
c. Indicate the maximum of the p.d.f., and explain why you are not worried that it is sometimes greater than 1. The p.d.
f. is g(t)=6t (1 − t) for 0≤t ≤1.
Get solution
6.6.21 Find and sketch the c.d.
f. associated with the given p.d.
f. and check that it increases to a value of 1. The p.d.
f. is f (x)=2x for 0 ≤ x ≤1 (as in Exercise 17).
Get solution
6.6.22 Find and sketch the c.d.
f. associated with the given p.d.
f. and check that it increases to a value of 1. ...
Get solution
6.6.23 Find and sketch the c.d.
f. associated with the given p.d.
f. and check that it increases to a value of 1. ...
Get solution
6.6.24 Find and sketch the c.d.
f. associated with the given p.d.
f. and check that it increases to a value of 1. The p.d.
f. is g(t)=6t (1 − t) for 0 ≤ t ≤1 (as in Exercise 20).
Get solution
6.6.25 Find the probability in two ways:
a. By integrating the given p.d.
f.
b. By using the c.d.
f. Make sure that your answers match. Shade the given areas on a graph of the p.d.
f. The p.d.
f. is f (x)=2x for 0≤ x ≤1 (as in Exercises 17 and 21). Find the probability that the measurement is between 0.2 and 0.6.
Get solution
6.6.27 Find the probability in two ways:
a. By integrating the given p.d.
f.
b. By using the c.d.
f. Make sure that your answers match. Shade the given areas on a graph of the p.d.
f. The p.d.
f. is ...for 1≤t ≤e (as in Exercises 19 and 23). Find the probability that the measurement is between 2.0 and 2.5.
Get solution
6.6.27 Find the probability in two ways:
a. By integrating the given p.d.
f.
b. By using the c.d.
f. Make sure that your answers match. Shade the given areas on a graph of the p.d.
f. The p.d.
f. is ...for 1≤t ≤e (as in Exercises 19 and 23). Find the probability that the measurement is between 2.0 and 2.5.
Get solution
6.6.28 Find the probability in two ways:
a. By integrating the given p.d.
f.
b. By using the c.d.
f. Make sure that your answers match. Shade the given areas on a graph of the p.d.
f. The p.d.
f. is g(t)=6t (1 − t) for 0 ≤ t ≤1 (as in Exercises 20 and 24). Find the probability that the measurement is between 0.5 and 0.8.
Get solution
6.6.29 Sketch the c.d.
f. associated with each of the following p.d.f.’s. ...
Get solution
6.6.30 Sketch the c.d.
f. associated with each of the following p.d.f.’s. ...
Get solution
6.6.31 Sketch the p.d.
f. associated with each of the following c.d.f.’s. ...
Get solution
6.6.32 Sketch the p.d.
f. associated with each of the following c.d.f.’s. ...
Get solution
6.6.33 Sketch the p.d.
f. associated with each of the following c.d.f.’s. ...
Get solution
6.6.34 Sketch the p.d.
f. associated with each of the following c.d.f.’s. ...
Get solution
6.6.35 Draw
histograms of the distributions of cell age from the assumptions in the
earlier problem. Find and graph the cumulative distribution. The cells in Section 6.4, Exercise 31, where Pr(cell is 0 day old) = 0.4 Pr(cell is 1 day old) = 0.3 Pr(cell is 2 days old) = 0.2 Pr(cell is 3 days old) = 0.1.
Get solution
6.6.36 Draw
histograms of the distributions of cell age from the assumptions in the
earlier problem. Find and graph the cumulative distribution. The
cells in Section 6.4, Exercise 32, where the cells with age greater
than or equal to 3 days have been eliminated from the culture.
Get solution
6.6.37
One
hundred pairs of plants are crossed, and each pair produces ten
offspring. The number of tall offspring is then counted. For the given
experiment, draw a histogram of the probability of each result, and find
the requested probability. ... Draw the histogram for
experiment a, and find the probability that between 4 and 6 plants
(inclusive) are tall.
Get solution
6.6.38
One
hundred pairs of plants are crossed, and each pair produces ten
offspring. The number of tall offspring is then counted. For the given
experiment, draw a histogram of the probability of each result, and find
the requested probability. ... Draw the histogram for
experiment b, and find the probability that between 4 and 6 plants
(inclusive) are tall.
Get solution
6.6.39
One
hundred pairs of plants are crossed, and each pair produces ten
offspring. The number of tall offspring is then counted. For the given
experiment, draw a histogram of the probability of each result, and find
the requested probability. ... Draw the histogram for
experiment c, and find the probability that between 4 and 6 plants
(inclusive) are tall.
Get solution
6.6.40
One
hundred pairs of plants are crossed, and each pair produces ten
offspring. The number of tall offspring is then counted. For the given
experiment, draw a histogram of the probability of each result, and find
the requested probability. ... Draw the histogram for
experiment d, and find the probability that between 4 and 6 plants
(inclusive) are tall.
Get solution
6.6.41 An
experiment to see which color of male birds female birds prefer is
repeated two times. The first time, females mate with red males with
probability 0.5, with blue males with probability 0.3, and with green
males with probability 0.2. The second time, females mate with red males
with probability 0.4, with blue males with probability 0.35, and with
green males with probability 0.25. At the end, the results of the two
experiments are combined. Suppose that 100 female birds were
tested in each experiment. Find the number out of 200 that mated with
each type of male, and convert the results into a probability
distribution.
Get solution
6.6.42 An
experiment to see which color of male birds female birds prefer is
repeated two times. The first time, females mate with red males with
probability 0.5, with blue males with probability 0.3, and with green
males with probability 0.2. The second time, females mate with red males
with probability 0.4, with blue males with probability 0.35, and with
green males with probability 0.25. At the end, the results of the two
experiments are combined. Suppose that 100 female birds were
tested in the first experiment and 200 females in the second. Find the
number out of 300 that mated with each type of male, and convert the
results into a probability distribution.
Get solution
6.6.43 An
experiment to see which color of male birds female birds prefer is
repeated two times. The first time, females mate with red males with
probability 0.5, with blue males with probability 0.3, and with green
males with probability 0.2. The second time, females mate with red males
with probability 0.4, with blue males with probability 0.35, and with
green males with probability 0.25. At the end, the results of the two
experiments are combined. Suppose that an equal number of female
birds were used in each experiment. Use the law of total probability to
find the probability distribution in the combined experiment.
Get solution
6.6.44 An
experiment to see which color of male birds female birds prefer is
repeated two times. The first time, females mate with red males with
probability 0.5, with blue males with probability 0.3, and with green
males with probability 0.2. The second time, females mate with red males
with probability 0.4, with blue males with probability 0.35, and with
green males with probability 0.25. At the end, the results of the two
experiments are combined. Suppose that three times as many
females birds were used in the first experiment. Use the law of total
probability to find the probability distribution in the combined
experiment.
Get solution
6.6.45 The p.d.
f. for the waiting time X until an event occurs often follows the exponential distribution (to be studied in Section 7.6), with the form ...for some positive value of α, defined for x ≥0. For each of the following values of α,
a. Find the c.d.
f.
b. Plot the p.d.
f. and c.d.
f.
c. Check that the p.d.
f. is the derivative of the c.d.
f.
d. Find Pr(X ≤1). Indicate this on both of your graphs.
e. Find Pr(1≤ X ≤3).
f. Find Pr(1 ≤ X ≤1.01) and show that it is approximately g (1) · 0.01. α =0.5.
Get solution
6.6.46 The p.d.
f. for the waiting time X until an event occurs often follows the exponential distribution (to be studied in Section 7.6), with the form ...for some positive value of α, defined for x ≥0. For each of the following values of α,
a. Find the c.d.
f.
b. Plot the p.d.
f. and c.d.
f.
c. Check that the p.d.
f. is the derivative of the c.d.
f.
d. Find Pr(X ≤1). Indicate this on both of your graphs.
e. Find Pr(1≤ X ≤3).
f. Find Pr(1 ≤ X ≤1.01) and show that it is approximately g (1) · 0.01. α =2.0.
Get solution
6.6.47 The p.d.
f. for the normal distribution shown in Example 6.6.13 has the rather unlikely looking formula ... Graph
this function. It is impossible to integrate this function, but figure
out how to get your computer to graph the associated c.d.
f. Use this to
compute the probability that the value lies between 45.0 and 75.0.
Get solution
