The week after week fix cost. X. for a specific machine has a likelihood thickness work given by 6x( 1 x), 0 0 in any

The week after week fix cost. X. for a specific machine has a likelihood thickness work given by

6x( 1 x), 0

with estimations in S100s.

a Find the mean and change of the dispersion of fix costs. b Find a span inside which these week after week fix expenses should lie in any event 75% of the time utilizing Tchebysheff's Theorem. c Find a span inside which these week by week fix costs lie precisely 75% of the time with precisely 50% of those not lying in the stretch over as far as possible and the other half underneath as far as possible. Contrast this stretch with the one got to some extent (b).

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In a hereditary qualities study, it was tracked down that the distance X between changes in a specific strand of DNA had a likelihood thickness work given by

I p.,) . (2- - v15' o,

with estimations in kb.

x > 0 in any case

a Find the mean and fluctuation of the dissemination of distances between transformations in this strand of DNA.

b Find a span inside which these distances between changes should lie in any event 75% of the time utilizing Tchebysheff's Theorem. c Find a span inside which these distances between transformations lie precisely 75% of the time with precisely 50% of those not lying in the stretch over as far as possible and the other half lying beneath as far as possible. Contrast this stretch with the one acquired partially (b).

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The pH level, a proportion of sharpness, is significant in investigations of corrosive downpour. For a specific lake. pattern estimations of acridity are made so that any progressions brought about by corrosive downpour can be noted. The pH for water tests from the lake is an irregular variable X, with likelihood thickness work

4 (7 x)2, 5 < x < 7 f (x) = 0, in any case.

a Find the mean, change. also, standard deviation of the conveyance of the pH of water in this lake.

b Find a careful stretch inside which 80% of the pH estimations should lie with half of the other 20% of the pH estimations lying underneath as far as possible and the other half lying over as far as possible.

c Would you hope to see a pH estimation more prominent than 6.5 frequently? Why?

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The extent of pollutions by weight X in certain copper mineral examples is an irregular variable having a likelihood thickness capacity of

f (x) = 12x2(1 x

0,

0 < x < I in any case.

a Find the mean and standard deviation of the appropriation of the extents of pollutants in these copper mineral examples. b The worth Y of 100 pounds of copper mineral is Y= 200(1-X) dollars. Track down the mean and standard deviation of the worth of 100 pounds of copper from this example.