Geometric Random Variables: 15% of the cars in a dealer's showroom have a sunroof.

Steven G

Steven G

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Dec 30, 2014
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Hi,
The solution manual and I disagree on the following problem. Can someone please be the referee?

Fifteen percent of the cars in a dealer's showroom have a sunroof. A sales-person starts showing you cars at random, one after the other. Let X be the number of cars with a sunroof that you see, before the first car that has no sunroof.
What is the probability distribution function of X?

The solution manual says that pX(x) = (.85)(.15)x-1, x=1,2... and 0 otherwise

I claim that pX(x) = (.85)(.15)x, x=1,2... and 0 otherwise.

I am sure that I am right but just checking.

 
Jomo said:
The solution manual and I disagree on the following problem. Can someone please be the referee?
Fifteen percent of the cars in a dealer's showroom have a sunroof. A sales-person starts showing you cars at random, one after the other. Let X be the number of cars with a sunroof that you see, before the first car that has no sunroof.
What is the probability distribution function of X?
The solution manual says that pX(x) = (.85)(.15)x-1, x=1,2... and 0 otherwise
I claim that pX(x) = (.85)(.15)x, x=1,2... and 0 otherwise.
I am sure that I am right but just checking.
Click to expand...
The probability that the first car you are shown has a no sunroof is 0.85.
 
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