4.30 The proportion of time Y that an industrial robot is in operation during a random variable with probability density function 2y, 0, f(y) = = 0≤ y ≤ 1, elsewhere. MU 90 a Find E(Y) and V (Y). b For the robot under study, the profit X for a week is given by X = 200Y and V(X). c Find an interval in which the profit should lie for at least 75% of the w
4.30 The proportion of time Y that an industrial robot is in operation during a random variable with probability density function 2y, 0, f(y) = = 0≤ y ≤ 1, elsewhere. MU 90 a Find E(Y) and V (Y). b For the robot under study, the profit X for a week is given by X = 200Y and V(X). c Find an interval in which the profit should lie for at least 75% of the w
A First Course in Probability (10th Edition)
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Pls help me solve 4.30
Transcribed Image Text:4.29
4.30
anoitudidad pildsdor
The temperature Y at which a thermostatically controlled switch turns on has probability density
function given by
a
b
Exercises 173
f(y) = {1/2, 59 ≤ y ≤ 61,
elsewhere.
Find E(Y) and V (Y).
The proportion of time Y that an industrial robot is in operation during a 40-hour week is a
random variable with probability density function
f(y) = {2y, 0≤ y ≤ 1,
0, elsewhere.
ONU 90
Find E(Y) and V (Y).
For the robot under study, the profit X for a week is given by X = 200Y
and V(X).
-
60. Find E(X)
c Find an interval in which the profit should lie for at least 75% of the weeks that the robot
is in use.
4.31 Daily total solar radiation for a specified location in Florida in October has probability density
function given by
f(y) = {(3/32)(y-2) (6-y), 2 ≤ y ≤6,
elsewhere,
with measurements in hundreds of calories. Find the expected daily solar radiation for October.
density function (measured in
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