Verify that f(x)=x/8 can serve as the probability density function of a continuous random variable which can take on any value in the interval from 0 to 4 ?

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Answer 1 · 2018-04-07T08:54:02

see below

for a function to be a pdf then

#int_(allx)f(x)dx=1#

must hold

#we have

#int_0^4(x/8)dx#

#=[x^2/16]_0^4#

#1/16{[x^2]^4-[x^2]_0}#

#=1/16{16-0)#

#=16/16=1#

#:.f(x)=x/8, [0,4]# can serve as a pdf