An electronics manufacturer tests its capacitors for leakage current X at the maximum specified voltage. If X is below 20 pA, the capacitor is declared good (event G). If X is above 30 pA, it's declared bad (event B). Capacitors with leakage between 20 and 30 pA are declared marginal (event M). 95% of the capacitors have dielectrics that are free of defects known as pinholes (event Q); for those capacitors the leakage current is a Gaussian random variable with mean 15 pA and standard deviation 5 pA. 5% of the capacitors have one or more dielectric pinholes (event P); for those capacitors the leakage current is a Gaussian random variable with mean 35 pA and standard deviation 5 pA. (a) What is the conditional PDF ffXX|QQ(xx)? (b) What is the conditional probability, P[M|Q], that the capacitor is declared marginal given that it has no pinholes? (c) What is the conditional probability P[Q|G] that it has no pinholes given that it tested good