Leave X and W alone the working and ensuing fix times ofa certain machine. Let Y = X + W

also, assume that the joint likelihood thickness of X and Yis

(a) Find the thickness of X.

(b) Find the thickness of Y.

(c) Find the joint thickness ofX and W

(d) Find the thickness of W

22))))

The standard deviation ot an arbitrary variable is the positive square root ot Its difference. Letting bull

also, cry signify the standard deviations of the arbitrary factors X and Y, we characterize the

relationship of X and Y by

cov(X, Y)

Corr(X, Y) =

(a) Starting with the disparity Var - F20, show that

bull

(b) Prove the disparity

1 Corr(X, Y) 1

(c) It is the standard deviation of X + Y, show that

l Corr(X,

23))

Each new book gave to a library should be prepared. Assume that the time it takes a custodian

to deal with a book has mean 10 minutes and standard deviation 3 minutes. Ita administrator has 40

books that should be prepared each in turn,

(a) surmised the likelihood that it will require over 420 minutes to handle every one of these books;

(b) surmised the likelihood that at any rate 25 books will be handled in the initial 240 minutes.

24))

Leave Xl and X2 alone autonomous mathematical arbitrary factors having a similar boundary p. Estimate

the worth of

Clue: Suppose a coin having likelihood p of coming up heads is persistently flipped. Ifthe second

head happens on flip number n, what is the contingent likelihood that the main head was on flip

number I, I = 1, .

Verity your speculation logically.