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Student Name: Student ID:

`q,`

PROBLEM 13 The diameter of a particle of contamination (in micrometers) is modeled with the probability density function

`f(x)=(2)/(x^(3))`

for

`x>1`

. Determine the following: a)

`P(x<2)`

[2 points] b) or

`x>8`

[2 points] c)

`x`

such that

`P(x`

)

```
[3 points]
```

(

```
d) Determine the cumulative distribution function.
[3 points]
Page 8 of 8
```