For a laboratory assignment, if the equipment is working, the density function of the observed outcome X is as shown below. Find the variance and standard deviation of X. (1) DEY 0
For a laboratory assignment, if the equipment is working, the density function of the observed outcome X is as shown below. Find the variance and standard deviation of X. (1) DEY 0
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.1: Measures Of Center
Problem 9PPS
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Transcribed Image Text:For a laboratory assignment, if the equipment is working, the density function of the
observed outcome X is as shown below. Find the variance and standard deviation of X.
f(x)
= 8
f
1
(4-x),
(4-x), 0<x<4,
otherwise
![The total time, measured in units of 100 hours, that a teenager runs her hair dryer over
a period of one year is a continuous random variable X that has the density function
below. Use the theorem below to evaluate the mean of the random variable
Y = 69X² + 43X, where Y is equal to the number of kilowatt hours expended annually.
Theorem: The expected value of the sum or
difference of two or more functions of a random
variable X is the sum or difference of the
expected values of the functions, as given by the
formula below.
E[g(X,Y) ±h(X,Y)] = E[g(X,Y)] ± E[h(X,Y)]
f(x)
=
X,
4
9
0<x< 1
1
-x 1<x<4
9
elsewhere](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbe7e575d-dfd7-411c-ad5f-62e2be64ba9f%2F024f51ac-7646-4415-bb6b-ffa72500ceaf%2Fbe8l5o4_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The total time, measured in units of 100 hours, that a teenager runs her hair dryer over
a period of one year is a continuous random variable X that has the density function
below. Use the theorem below to evaluate the mean of the random variable
Y = 69X² + 43X, where Y is equal to the number of kilowatt hours expended annually.
Theorem: The expected value of the sum or
difference of two or more functions of a random
variable X is the sum or difference of the
expected values of the functions, as given by the
formula below.
E[g(X,Y) ±h(X,Y)] = E[g(X,Y)] ± E[h(X,Y)]
f(x)
=
X,
4
9
0<x< 1
1
-x 1<x<4
9
elsewhere
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