Find the conditional pdf of Y, given X = x. Compare this to the marginal pdf of Y. Are air temperature and engine warm-up time independent?
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Let X denote 0.025 × the ambient air temperature (˚C) and let Y denote the time (min) that it takes for a diesel engine to warm up. Assume that (X, Y) has joint probability density
f(x,y) = cx (1 − x)(6 + 5x − 4y), for 0 < x < 1, 0 < y < 0.5.
Find the conditional
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