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Suppose that the probability density function of the length of computer cables is f (x) = 2x/(52) for x between 0 and 5 meters. Determine the standard deviation of the cable length. Please enter the answer to 2 decimal places.

Question

Suppose that the probability density function of the length of computer cables is f (x) = 2x/(52) for x between 0 and 5 meters. Determine the standard deviation of the cable length. Please enter the answer to 2 decimal places.

check_circleAnswer
Step 1

Let X be the continuous random variable which denotes the length of the computer cables.

 

The probability density function of X is given by,

2x
f(x)
52
2x for 0X <5
25
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2x f(x) 52 2x for 0X <5 25

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Step 2

The standard deviation of X is ca...

SD(x) E(x)-(E(x)
(1)
Now, find E(X) and E(X2) as shown below:
E(X)-()
E(x)=x)
0
2 2
2 5
25%
250
0
2
2
25 3
25 4
2
2
25x3
25x4
2
2
[125]
25 x3
x625]
25x4
10
25
2
|I
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SD(x) E(x)-(E(x) (1) Now, find E(X) and E(X2) as shown below: E(X)-() E(x)=x) 0 2 2 2 5 25% 250 0 2 2 25 3 25 4 2 2 25x3 25x4 2 2 [125] 25 x3 x625] 25x4 10 25 2 |I

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