So I'll switch these b y the X when we get point of a K in a row from 20 to 26 then taking anti derivative of X squared, we get X squared. Let's actually integrate with respect to why first. Once again, you can split this up into to integral what? Instead of doing that, I'll evaluated from the inside out.
#Average tire psi plus
Um, okay, which we found in the previous part Times X squared plus y squared dx dy y. This is going to be the integral I don't really care about 10 points from 20 to 26 and you go from 2026. So we're looking for the probability that each tire then filled. Now it therefore follows that K is going equal to one over this So three over create zero 000 380,000 Now in part B rest to find the probability that both tires are under filled sort of call that each front tires must be filled to a pressure of 26 PSC. This comes out to be approximately 19,000 over three. Why square to d Y and evaluating this? We can have these two together since they're really the same integral with different dummy variables and we get 20 k and taking the anti derivative and evaluating we get well 30 cubed minus 20 Cute over three. So this is going to be equal to en que After taking the Negro with respect to y first in the growth from 20 to 30 x squared the X plus 10-K and I go from 20 to 30. So this is going to be a K times integral from 20 to 30 and a girl from 20 to 30 x squared DX plus k times in enrollment 20 to 30 to grow from 20 to 30. We get k times X squared plus y squared dx dy y we can break this up into two into girls. This is equal to integral from because it's equal to zero outside these bounds, integral from 20 to 30 they grow from 20 to 30 and then plugging in. So we have that one is equal to in a girl from negative infinity to infinity in a rough negative community to infinity Um, our probability density function f of x y dx dy y. And why between 20 and 30 and zero Otherwise, in part a where has to find the value of K So to do this well, we know that the some overall outcomes has to be one. Where X is there an invariable for the right tire? And why is the one for the left tire which have a joint Excuse me? Partial density function probability, density function f of X y equals K times X squared plus y squared for X between 20 and 30. And they were told that the actual air pressure each tire is a random variable.
We're told that each front tire the vehicle is supposed to be filled to a pressure of £26 per square inch.
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