For a costly thing, two monitors should support every thing before it is dispatched. Let X1, the time needed for the main reviewer to audit a thing, and X2, the time needed for the subsequent assessor to survey a thing, be free, outstanding arbitrary factors with boundary O. Let 1r.i be the extent of the all out examination time taken by the main auditor and Y2 be the all out time taken by the reviewers. a Find the joint likelihood dissemination of 111 and Y2.

b Find the minimal circulation of c Find the minor appropriation of Y2. d Are V.1 and Y2 free? Legitimize your answer.

6))

Assume that X1. X2 X,7 comprise an arbitrary example from a uniform dissemination over the stretch (0, e) for some steady e > 0. a Find the likelihood thickness work for X0). b Find E(X0)). c Find V(Xel)). d Find a steady b with the end goal that E(bX(n)) = 0. e Find the likelihood thickness work for the reach R = Xp) - X(1). f Find E(R).

7))

Resistors of a specific sort have protections that normal 200 ohms with a standard deviation of 10 ohms. Assume that 25 of these resistors are to be utilized in a circuit. a Find the likelihood that the normal opposition of the 25 resistors is somewhere in the range of 199 and 202 ohms.

b Find the likelihood that the all out opposition of the 25 resistors doesn't surpass 5100 ohms. [Hint: Notice that

n P (EXi > a = P (id > a) = P(g > alt?) i=1 for the circumstance described.] c What suppositions are important for the appropriate responses in parts (a) and (b) to be acceptable approximations?

8))

Assume that X.1. X2 , . . Xn are autonomous irregular factors, each with a mean of N1 and a fluctuation of a2 1 . Assume that Y1, Y2 Y are autonomous arbitrary factors, each with a mean of p2 and a change of a2 2 . Show that, as n.. the irregular variable

(X-Y)- (l-2)

1(af c2 )/n

meets in dissemination toward a standard typical arbitrary variable.