Measurements of scientific systems are always subject to variation, some more than others. There are many structures for measurement error, and statisticians spend a great deal of time modeling these errors. Suppose the measurement error X of a certain physical quantity is decided by the density function given below. Complete parts (a) through (c). F(x) = { *(4-x²), -1≤x≤1 elsewhere
Measurements of scientific systems are always subject to variation, some more than others. There are many structures for measurement error, and statisticians spend a great deal of time modeling these errors. Suppose the measurement error X of a certain physical quantity is decided by the density function given below. Complete parts (a) through (c). F(x) = { *(4-x²), -1≤x≤1 elsewhere
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![Measurements of scientific systems are always subject to variation, some more than others. There are many
structures for measurement error, and statisticians spend a great deal of time modeling these errors. Suppose the
measurement error X of a certain physical quantity is decided by the density function given below. Complete parts (a)
through (c).
1801- {x (4-1²]).
f(x) =
k(4-x²), -15xs1
elsewhere
(a) Determine k that renders f(x) a valid density function.
k= (Type an integer or a simplified fraction.)
2
W|N
(b) Find the probability that a random error in measurement is less than
3
The probability is
(Type an integer or decimal rounded to three decimal places as needed.)
(c) For this particular measurement, it is undesirable if the magnitude of the error (i.e., |x|) exceeds 0.75. What is the
probability this occurs?
The probability is
(Type an integer or decimal rounded to three decimal places as needed.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F985a3bdb-5f82-4661-b745-6b8845900495%2F66f19fa1-f2d4-4719-bae0-2e20f801f933%2Focfdc3_processed.png&w=3840&q=75)
Transcribed Image Text:Measurements of scientific systems are always subject to variation, some more than others. There are many
structures for measurement error, and statisticians spend a great deal of time modeling these errors. Suppose the
measurement error X of a certain physical quantity is decided by the density function given below. Complete parts (a)
through (c).
1801- {x (4-1²]).
f(x) =
k(4-x²), -15xs1
elsewhere
(a) Determine k that renders f(x) a valid density function.
k= (Type an integer or a simplified fraction.)
2
W|N
(b) Find the probability that a random error in measurement is less than
3
The probability is
(Type an integer or decimal rounded to three decimal places as needed.)
(c) For this particular measurement, it is undesirable if the magnitude of the error (i.e., |x|) exceeds 0.75. What is the
probability this occurs?
The probability is
(Type an integer or decimal rounded to three decimal places as needed.)
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