16) me of a sheet metal crimper has the ears 1 10 05 05 10 15 20 20 15 Determine

Question

16) me of a sheet metal crimper has the ears 1 10 05 05 10 15 20 20 15 Determine the expected lifetime of the crimper, given that it lasts fewer than 5 years. a) 2.3 b) 2.5 )2.6 d) 2.8 e)3.0 17) In (16), suppose an insurance policy pays the factory according to the formula: payment-$1000 x (8-lifetime) Thus, if the crimper lasts 5 years, the factory receives a payment of $1000(8-5)-$3000. Determine the expected payment under this policy a)3200 b) 3300 c)3500 d) 3600 e) 3800 problems 18 -24 refer to the joint pmf below giving joint probabilities for the numbers of BMW's (B) & Honda's (H) sold in one day at Finell Bros. 5 6

Explanation / Answer

Let us denote the lifetime of the crimper be X

P(X= x/ X<5) = P(X=x and X<5)/P(X<5)

P(X<5) = P(X=1) + P(X=2)+ P(X=3)+ P(X=4)

= 0.05 + 0.10 +0.15 +0.20 = 0.5

P(X=1/X<5) = P(X=1 and X<5)/P(X<5) = P(X=1)/0.5 = 0.05/0.5 = 0.1

P(X=2/X<5) = P(X=2 and X<5)/P(X<5) = P(X=2)/0.5 = 0.10/0.5 = 0.2

P(X=3/X<5) = P(X=3 and X<5)/P(X<5) = P(X=3)/0.5 = 0.15/0.5 = 0.3

P(X=4/X<5) = P(X=4 and X<5)/P(X<5) = P(X=4)/0.5 = 0.20/0.5 = 0.4

expected lifetime of crimper, given that it lasts fewer than 5 years

=1*P(X=1/X<5) +2*P(X=2/X<5)+3*P(X=3/X<5)+4*P(X=4/X<5)

= 1*0.1+2*0.2+3*0.3+4*0.4 = 3

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