The proportion of time X that an industrial robot is in operation during a 40-hour work week is a random variable with probability density function 2x 0

MATLAB: An Introduction with Applications
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The proportion of time X that an industrial robot is in operation during a 40hour work-week is a random variable with probability density function.

Note: The probability density function is shown in img3.jpg

a) Find E(X) and V(X)

b) For the robot understudy, the profit Y for a week is given by

    Y = 200X -60

c) Find an interval in which the profit should lie for at least 75% of the weeks that the robot is in use. [Hint: Use Tchebysheff's theorem.]

The proportion of time X that an industrial robot
is in operation during a 40-hour work week is a
random variable with probability density function
2x 0<x<1
f(x) =
elsewhere
bng
a Find E(X) and V(X).
b For the robot under study, the profit Y for a
week is given by
Y = 200X -60
Find E(Y) and V(Y).
c Find an interval in which the profit should lie
for at least 75% of the weeks that the robot is
in use. [Hint: Use Tchebysheff's theorem.]
Transcribed Image Text:The proportion of time X that an industrial robot is in operation during a 40-hour work week is a random variable with probability density function 2x 0<x<1 f(x) = elsewhere bng a Find E(X) and V(X). b For the robot under study, the profit Y for a week is given by Y = 200X -60 Find E(Y) and V(Y). c Find an interval in which the profit should lie for at least 75% of the weeks that the robot is in use. [Hint: Use Tchebysheff's theorem.]
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