The ph of water samples from a specific lake is a random variable y with probability density function given by f (y) = $ (3/8)(7 − y) 2 , 5 ≤ y ≤ 7, 0, elsewhere. a find e(y ) and v(y ). b find an interval shorter than (5, 7) in which at least three-fourths of the ph measurements must lie. c would you expect to see a ph measurement below 5.5 very often? why?

Given that the ph of water samples from a specific lake is a random variable y with probability density function given by



Part A:



Part B:






Part C:

Let the required interval be (5, b), then



Therefore, an interval shorter than (5, 7) in which at least three-fourths of the ph measurements must lie is (5, 5.74).

Part D:



Since, the probability that a ph measurement is below 5.5 significant (i.e. 57.75%), we would expect to see a ph measurement below 5.5 very often.