A company has two types of machine that run 24 hours a day, 7 days a week. Type A machine breaks down on average 10 breakdowns per day. This is equivalent to saying the mean wait time per breakdown is days per breakdown. For type B machine, the mean wait time between breakdowns is 0.7 days per breakdown.

For each type of machine, assume breakdowns occur as a time homogeneous Poisson process, so that for each type of machine the waiting time for a breakdown has exponential distribution, but with differing parameters depending on whether the machine is type A or type B.

Suppose 25% of the machines at this company are type A.

You observe a machine but cannot tell what type it is. But you do observe that within the next 5 hours it does not break down. What is the posterior probability this is a type A machine? Answer as a decimal accurate to 4 decimal places.

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a vertical line intersects the graph of g(x,y) = 0 at two points. what conclusion follows about the function f(x) implicitly defined by g(x,f(x)) = 0?

the domain of f(x) cannot include the x coordinate of any such vertical line.

informally, f(x) is not a function, and

g(x,y)=0 cannot be solved for y uniquely.

the relation r = {(x,y) such that g(x,y) = 0} is a function if

for all (a,b) ∊ r and (c,d) ∊ r, a=c implies b=d.

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