Probability of 2 jointly uniform random variables

X~U(2, 2.5), Y~U(2,2.3) f(x) = 2 f(y) = 10/3

I found f(x,y) = 20/3

What is the probability that X and Y are within 0.1 of each other?

I think it should be P(|X-Y|<0.1), but how can I write the limit of the integral in this case?

Thanks.

Quote:

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Originally Posted by armeros

X~U(2, 2.5), Y~U(2,2.3) f(x) = 2 f(y) = 10/3

I found f(x,y) = 20/3

What is the probability that X and Y are within 0.1 of each other?

I think it should be P(|X-Y|<0.1), but how can I write the limit of the integral in this case?

Thanks.

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I see you have assumed that X and Y are independent ..... You need to integrate over the support of the joint pdf in the region bounded by the lines y = x + 0.1 and y = x - 0.1 (draw a diagram).

I just got it. The answer is 0.36667 = 11/30 Thank you very much.