# Thread: Probability for a Two-dimensional Discrete random variable

1. ## Probability for a Two-dimensional Discrete random variable

Hi all,

I hope someone can help me a bit facing this problem. I have many item samples from a database (let's say 1000 for example) with two attributes: a price from a range of possible prices (0 to 8000€ for example) and color (only two options, black or white).

I got all these samples and I assumed they represent a Two-dimensional discrete aleatory variable, where one variable (X) is the price, and the other (Y) is the color. Having this I calculated and plotted the Joint density function being the price the x-axis, probability the y-axis and the color the z-axis. The graph seems to follow (roughly) a Normal distribution. In addition I calculated and plotted as well the Conditional Density function fx(x|Y=black) and the Percentiles for black and white options. Black items seem to gather in low prices.

My question is: having all this information, how can I predict what's the probability of being 'black' (unknown) for a new incoming sample with a certain price (known). I'd like to set a probability percentage threshold to trigger a warning for 'high possibility of new incoming item being black'

Thanks a lot,

Nacho

2. ## Re: Probability for a Two-dimensional Discrete random variable

Your problem should be related to a classification problem. You can start to read from here

https://en.wikipedia.org/wiki/Probab...classification

and see if there are any inspirations for you. There are lots of methods listed in that page which you can consider.

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