SOLUTION: The cumulative distribution function of the random variable X is given by: F(x)={(1- 9/x^2 ) for( 3 < x )otherwise0 Find the probability density function for the random variab

Algebra ->  Probability-and-statistics -> SOLUTION: The cumulative distribution function of the random variable X is given by: F(x)={(1- 9/x^2 ) for( 3 < x )otherwise0 Find the probability density function for the random variab      Log On


   



Question 1029370: The cumulative distribution function of the random variable X is given by:
F(x)={(1- 9/x^2 ) for( 3 < x )otherwise0
Find the probability density function for the random variable X.
compute p(X≤ 5) and p( 8< X )
Find the expected value for the random variable X.

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=dF%2Fdx=18%2Fx%5E3 for x%3E3
f%28x%29=0 for x%3C=3
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So then,
p%28x%3C=5%29=int%28%2818%2Fx%5E3%29%2Cdx%2C3%2C5%29=F%285%29-F%283%29=1-9%2F25-0=16%2F25
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p%28x%3C=8%29=F%288%29-F%283%29=1-9%2F64-0=55%2F64
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E=int%28%28x%2Af%28x%29%29%2Cdx%2C3%2Cinfinity%29
E=int%28%2818%2Fx%5E2%29%2Cdx%2C3%2Cinfinity%29
E=-18%2Fx%2BC
E=0-%28-18%2F3%29
E=6