A continuous random variable X that can assume values between x=2 and x=4 has a density function given by

f(x)=x+1/8

Show that P (2<x<4) =1

Find P(X<3.5)

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- Dec 27th 2007, 09:53 AMMS BATOOLStatistics and probability
A continuous random variable X that can assume values between x=2 and x=4 has a density function given by

f(x)=x+1/8

Show that P (2<x<4) =1

Find P(X<3.5) - Dec 27th 2007, 09:59 AMcolby2152
Integrate f(x) from 2 to 4 and you get an answer of 6.25, not 1. Therefore, it is not a correct pdf. However, if you meant $\displaystyle f(x)=\frac{x+1}{8}$, it does satisfy having an integral of one. To find the probability that x is less than 3.5, integrate the pdf from 2 to 3.5.