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 function. f(x,y) = 1.6x (1 − x)(6 + 5x − 4y), for 0 < x < 1, 0 < y < 0.5. What is the probability that the air temperature will be less than 20˚C (so X ≤ 0.5) and it will take no more than 0.2 minute for the engine to warm up?

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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 function.

f(x,y) = 1.6x (1 − x)(6 + 5x − 4y), for 0 < x < 1, 0 < y < 0.5.

What is the probability that the air temperature will be less than 20˚C (so X ≤ 0.5) and it will take no more than 0.2 minute for the engine to warm up?

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