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Okay so I am having some trouble with this problem. Let's say two variables G and C jointly follow bivariate normal distribution. With G having mean 480 and SD 100 and C having mean 320 and SD 60. Now I can solve problem like P(G < 360) or P(G - C < 400). What I'm having trouble on is P(G = 400). How do I find the probability that a variable is equal to something when it follows this distribution? T

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Are you perhaps asking about conditional probability?

With continuous RVs, $P(X=k)=0$. If you ask about one RV in a joint distribution, that doesn't really make things different.

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  • $\begingroup$ See I had problems that asked about conditional probability in this assignment and I was able to solve those. I was just confused on this question because of the fact it asked me P(X=k). Is there a way to solve P(X=k) if it were just one random variable that is normally distributed? $\endgroup$
    – ms25297
    Oct 19, 2017 at 5:24
  • $\begingroup$ Ignore the joint distribution. Imagine a single RV. Now imagine that you have a circle that goes from 0 to 1, with an arrow you can spin in the middle (sort of like a roulette wheel). The probability distribution would, in that case, be a uniform distribution when you spin the arrow: it lands anywhere with equal chance. Now - and this is a bit hard mathematically - the probability of any single number coming up on a spin (like $\sqrt \pi /10$ is zero. the probability it lies between, say, 0 and 0.5 is 50%. It will land on a number, but the probability of that number is zero. Follow? $\endgroup$
    – eSurfsnake
    Oct 19, 2017 at 5:30
  • $\begingroup$ Yeah I believe I understand it now, Thank you for your help. $\endgroup$
    – ms25297
    Oct 19, 2017 at 5:39
  • $\begingroup$ You are more than welcome. $\endgroup$
    – eSurfsnake
    Oct 19, 2017 at 5:46

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