jnu sss 2018, stats question

[soimmoi]

Mean x= 1 ; Var X= 9
Y= 3X+6
W= -3X+6
which of following is true
a) Cov. W&Y cannot be calculated
b) cov W&Y = -9
c) correlation W&y =-1
d) correlation W&y = 1

I'm getting b as answer, is it correct?

[MomoChan]

 The answer will be (C) according to my calculations .
E(YW) = -54 , E(Y) = 9 , E(W) = 3 , Cov (Y,W) = -81 , Var(Y) = 81 , Var(W) = 81 , Corr. coffe = -1

[soimmoi]

thank you

[soimmoi]

a computer has two processors. the probability that processor 1 works is ¾ and the probability that processor 2 works is 7/8. the computer will function if processor 1 works or 2 works or both works. find probability thta processor 1 works given thta computeris functional?
6/13?

[MomoChan]

According to my calculations it should be 24/31 .
P(Processor one working given computer is functional) = 3/4 * 1/8 + 3/4 * 7/8 = 24/32
P(Computer functional) = 3/4* 1/8 + 7/8 * 1/4 + 3/4 * 7/8 = 31/32

Therefore : 24/32
                 -------    = 24/31
                 31/32  

[soimmoi]

hey what I think is P( functional) = P(A) or P(B) or both
so, it should be P(A) + P(B) - P(A intersection b)
3/4 + 7/8 - 3/4*7/8

[MomoChan]

P(A) or P(B) or Both means P(A) + P(B) + P(A intersection B)
i.e either A or B or Both works .
What you are doing is that you're eliminating the both part