An electronic system has one each of two different types of components in joint oper- ation. Let Y₁ and Y₂ denote the random lengths of life, in hundreds of hours, of the components of type I and type II, respectively. The joint density function is given by: f(y₁, y2) = [(1/8)y₁e-(3₁+2)/²_ if y₁ >0, y2 > 0 elsewhere 0 (a) Verify that f(y₁, y2) is a probability density function. (b) Find P(Y₁ > 1, Y2₂ > 1). (c) Find the probability that a component of type II will have a life length in excess of 200 hours. (d) Is fy₁, y₂ (y1, y2) = fy₁ (₁) fy₂ (Y2)? (e) One way to measure the relative efficiency of the two components is to compute the ratio Y₂/Y₁. Find E(Y₂/Y₁).

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