discrete random variable

Statement of the problem:
Discrete random variable x is described by the PDF:
px(xo) = (5-xo)/12 if xo = 0,1,2
px(xo) = 0 otherwise

let d1, d2, d3,...dN represent N successive independent experimental values of random variable x.

Determine the probability that d1>d2
Determine the probability that d1+d2+...dN <= 1.0

Quote:

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Originally Posted by rbenito

Statement of the problem:
Discrete random variable x is described by the PDF:
px(xo) = (5-xo)/12 if xo = 0,1,2
px(xo) = 0 otherwise

let d1, d2, d3,...dN represent N successive independent experimental values of random variable x.

Determine the probability that d1>d2
Determine the probability that d1+d2+...dN <= 1.0

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p(d1>d2)=p(d2>d1)

and

1=p(d1>d2)+p(d1=d2)+p(d2>d1)= 2p(d1>d2)+p(d1=d2)

so:

p(d1>d2)=[1-p(d1=d2)]/2

p(d1=d2)=p(d1=0)p(d2=0) + p(d1=1)p(d2=1) + p(d1=2)p(d2=2)

............ =p(d1=0)^2+p(d1=1)^2+p(d1=2)^2

RonL