Jng-uistance telephone conversation. ASsume thal the density for X is given by f(x) = (1/10)e-x/10 x>0 (a) Verify that f is a density for a continuous random variable. (b) Assuming that f adequately describes the behavior of the random variable X, find the probability that a randomly selected call will last at most 7 minutes; at least 7 minutes; exactly 7 minutes. (c) Would it be unusual for a call to last between 1 and 2 minutes? Explain, based on the probability of this occurring. (d) Sketch the graph of f and indicate in the sketch the area corresponding to each of the probabilities found in part (b). 4. Some plastics in scrapped cars can be stripped out and broken down to recover the chemical components. The greatest success has been in processing the flex- ible polyurethane cushioning found in these cars. Let X denote the amount of this material, in pounds, found per car. Assume that the density for X is given by 1 1 f(x) = 25
Jng-uistance telephone conversation. ASsume thal the density for X is given by f(x) = (1/10)e-x/10 x>0 (a) Verify that f is a density for a continuous random variable. (b) Assuming that f adequately describes the behavior of the random variable X, find the probability that a randomly selected call will last at most 7 minutes; at least 7 minutes; exactly 7 minutes. (c) Would it be unusual for a call to last between 1 and 2 minutes? Explain, based on the probability of this occurring. (d) Sketch the graph of f and indicate in the sketch the area corresponding to each of the probabilities found in part (b). 4. Some plastics in scrapped cars can be stripped out and broken down to recover the chemical components. The greatest success has been in processing the flex- ible polyurethane cushioning found in these cars. Let X denote the amount of this material, in pounds, found per car. Assume that the density for X is given by 1 1 f(x) = 25
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![Jng-uistance telephone conversation.
ASsume thal the
density for X is given by
f(x) = (1/10)e-x/10
x>0
(a) Verify that f is a density for a continuous random variable.
(b) Assuming that f adequately describes the behavior of the random variable
X, find the probability that a randomly selected call will last at most
7 minutes; at least 7 minutes; exactly 7 minutes.
(c) Would it be unusual for a call to last between 1 and 2 minutes? Explain,
based on the probability of this occurring.
(d) Sketch the graph of f and indicate in the sketch the area corresponding to
each of the probabilities found in part (b).
4. Some plastics in scrapped cars can be stripped out and broken down to recover
the chemical components. The greatest success has been in processing the flex-
ible polyurethane cushioning found in these cars. Let X denote the amount of
this material, in pounds, found per car. Assume that the density for X is given by
1 1
f(x) =
25 <x< 50
In 2 x
(a) Verify that f is a density for a continuous random variable.
(b) Usefto find the probability that a randomly selected auto will contain be-
tween 30 and 40 pounds of polyurethane cushioning.
(c) Sketch the graph of f, and indicate in the sketch the area corresponding to
the probability found in part (b).
5. (Continuous uniform distribution.) A random variable X is said to be uni-
formly distributed over an interval (a, b) if its density is given by
1
f(x) =
a<x<b
%3D
b- a
(a) Show that this is a density for a continuous random variable.
(b) Sketch the graph of the uniform density.
(c) Shade the area in the graph of part (b) that represents P[X< (a + b)/2].
(d) Find the probability pictured in part (c).
(e) Let (c, d) and (e, f) be subintervals of (a, b) of equal length. What is the re-
lationship between P[c <X sd] and P[e <X<f]? Generalize the idea
suggested by this example, thus justifying the name "uniform" distribution.
0. If a pair of coils were placed around a homing pigeon and a magnetic field
was applied that reverses the earth's field, it is thought that the bird would be-
come disoriented. Under these circumstances it is just as likely to fly in one
direction as any other, Let 0 denote the direction in radians of the bird's ini-
tial flight. See Fig. 4.18. 0 is uniformly distributed over the interval [0, 27].
(a) Find the density for 0.
in](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc074fc7e-4e48-46f1-bfc4-aee6ba4e6262%2F3c71a4be-9b34-4095-84a7-00accbf12bed%2Ffurx2gl.jpeg&w=3840&q=75)
Transcribed Image Text:Jng-uistance telephone conversation.
ASsume thal the
density for X is given by
f(x) = (1/10)e-x/10
x>0
(a) Verify that f is a density for a continuous random variable.
(b) Assuming that f adequately describes the behavior of the random variable
X, find the probability that a randomly selected call will last at most
7 minutes; at least 7 minutes; exactly 7 minutes.
(c) Would it be unusual for a call to last between 1 and 2 minutes? Explain,
based on the probability of this occurring.
(d) Sketch the graph of f and indicate in the sketch the area corresponding to
each of the probabilities found in part (b).
4. Some plastics in scrapped cars can be stripped out and broken down to recover
the chemical components. The greatest success has been in processing the flex-
ible polyurethane cushioning found in these cars. Let X denote the amount of
this material, in pounds, found per car. Assume that the density for X is given by
1 1
f(x) =
25 <x< 50
In 2 x
(a) Verify that f is a density for a continuous random variable.
(b) Usefto find the probability that a randomly selected auto will contain be-
tween 30 and 40 pounds of polyurethane cushioning.
(c) Sketch the graph of f, and indicate in the sketch the area corresponding to
the probability found in part (b).
5. (Continuous uniform distribution.) A random variable X is said to be uni-
formly distributed over an interval (a, b) if its density is given by
1
f(x) =
a<x<b
%3D
b- a
(a) Show that this is a density for a continuous random variable.
(b) Sketch the graph of the uniform density.
(c) Shade the area in the graph of part (b) that represents P[X< (a + b)/2].
(d) Find the probability pictured in part (c).
(e) Let (c, d) and (e, f) be subintervals of (a, b) of equal length. What is the re-
lationship between P[c <X sd] and P[e <X<f]? Generalize the idea
suggested by this example, thus justifying the name "uniform" distribution.
0. If a pair of coils were placed around a homing pigeon and a magnetic field
was applied that reverses the earth's field, it is thought that the bird would be-
come disoriented. Under these circumstances it is just as likely to fly in one
direction as any other, Let 0 denote the direction in radians of the bird's ini-
tial flight. See Fig. 4.18. 0 is uniformly distributed over the interval [0, 27].
(a) Find the density for 0.
in
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