Suppose that X and Y are independent random variables, where X is normally distributed with mean 45 and standard deviation 0.5 and Y is normally distributed with mean 20 and standard deviation 0.1.(adsbygoogle = window.adsbygoogle || []).push({});

(a) [tex] Find \ P(40 \leq X \leq 50, \ 20 \leq Y \leq 25). [/tex] Ans. ~0.5

(b) [tex] Find \ P(4(X-45)^2+100(Y-20)^2 \leq 2). [/tex] Ans. ~0.632

Part (a) is easy. I used Maple to find the double integral of the joint density function from [tex] 40 \leq X \leq 50, \ 20 \leq Y \leq 25. [/tex] and I get 0.5

Part (b) is my problem. How do I find the limits of integration? I tried solving for X and Y but I couldn't get that to work. Am I missing something easy here? Please please please help me! This assignment is due tomorrow and I've been stuck on this problem for days.

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# Homework Help: Urgent Math Help - Normally distributed probability density function

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