Question

In a certain production company, according to the test results from a motherboard 50% of board failures are caused by assembly defects, 30% by electrical components, and 20% by mechanical defects. Suppose that 10 boards fail independently. Consider that the number of assembly, electrical, and mechanical defects among the 10 boards are respectively denoted by the random variables X, Y, and Z. a. P(X=5,Y=3.2=2) b. PIX=8)= c. P[X=8|Y=1)= d. PX=7,Y=112=2)=

Answer 1

Given data motherboard Sos. board failured Eplectrical Components 301. mechanical defects 10 boards failed independently Random variables x, 482 Lovce assembly (= hoof defects among lo bords Electrical y = hoool defects bhong lo bords z = No. of mechanical defects among lo boards P(x=10=0.5 ply=1)=0.3 P (2=1) = 0.2 Here lo boards failed independently So, OXY = y)=PX=30) R4=y) PCX= ye/y34) = P(x = 34,434) ) PCY=) =P CR=2) P(X=nlap(x-uh independent of trails P -5, 4-912=9) =P(X=5) PCY-3) (2-9) = (0.55 (0.373 (6.22 a) = 0.0000 3375 = 3.375 X 105 CS Scanned with CamScanner

b) ९(x-8) (०. 58 = 0.0039 3963 ९ (x - ९ (५%) = ९ (X-8) 0.0039 - २१ ॥ d) ९ (१31 17-1) - ९ (7% 14.10 - ९ (1) ९ (५) (0.5) (63) 0.002344 234+113 CS Scanned with CamScanner