a. Surface mount type aluminium electrolytic capacitors have high reliability, long life, low impedance, and high ripple current and applied for in-vehicle equipment. A 50 V, 100 µF capacitor with a...

FULL ANSWER PLEASE

Extracted text: a. Surface mount type aluminium electrolytic capacitors have high reliability, long life, low impedance, and high ripple current and applied for in-vehicle equipment. A 50 V, 100 µF capacitor with a case size of 8.0 mm diameter and 10.2 mm length, has a mean endurance of 2000 hours. i. Based on conducted product test, the obtained endurance standard deviation of the manufactured capacitors is 50 hours. Determine the highest probability that the manufactured capacitor can only endure usage until 1800 hours. It is known that the distribution is symmetric about the mean. Production Line 1, x and Production Line 2, y are the two different capacitor production lines and, therefore, independent. Therefore, we may consider that they have independent random variables. For these production lines having joint probability distribution as shown in Table Q2a.ii, find E(3X – 2Y) and E (XY). Table Q2a.ii f(x. y) 4 1 0.10 0.15 y 3 0.30 0.20 0.10 0.15 iii. The variance of Production Line 1, x and Production Line 2, y is 6 and 4, respectively. Calculate the variance of the random variable Z = -2X + 4Y – 3.