SOLUTION: the probability density function of the random variable X is given by : f(x) ={&#9608;(@1/5 for2<x<7@ @0 elsewhere )&#9508;

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Question 1100379: the probability density function of the random variable X is given by :
f(x) ={█(@1/5 for2
Verify that the area under the curve is 1.
Find P(3 c) Find the expected value of the random variable X.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=1%2F5 for 2%3Cx%3C7
If you integrate over all values,
P=int%28f%28x%29%2Cdx%2Cx=0%2Cinfinity%29

P=0%2Bint%28f%28x%29%2Cdx%2Cx=2%2C5%29%2B0
P=int%28f%28x%29%2Cdx%2Cx=2%2C7%29
P=%281%2F5%29%287-2%29
P=%281%2F5%29%285%29
P=1
.
.
.
P=int%28%281%2F5%29%2Cdx%2Cx=3%2C5%29
P=%281%2F5%29%285-3%29
P=%281%2F5%29%282%29
P=2%2F5
.
.
.
P=int%28f%28x%29%2Cdx%2Cx=0%2C5%29
P=int%28f%28x%29%2Cdx%2Cx=0%2C2%29%2Bint%28f%28x%29%2Cdx%2Cx=2%2C5%29
P=0%2Bint%28f%28x%29%2Cdx%2Cx=2%2C5%29
P=int%28f%28x%29%2Cdx%2Cx=2%2C5%29
P=%281%2F5%29%285-2%29
P=%281%2F5%29%283%29
P=3%2F5