The diameter of a particle of contamination (in micrometers) is modeled with the probability density function f (x) = Determine the following (round all of your answers to 3 decimal places): (a) P(X < 3) i (b) P(X>6) 0.027 (c) P(3 < X < 7) 0.091 (d) P(X <3 or X> 7) i ! (e) Determine x such that P(X < x) = 0.90. 3.162 ! - for x > 1.

6. Roughly, speaking, we can use probability density functions to model the likelihood of an event occurring. Formally, a probability density function on (-x, o0) is a function f such that f(r) 20 and (2) = = 1. (a) Determine which of the following functions are probability density functions on the (-x0, 00). fr-1 00 (b) We can also use probability density functions to find the erpected value of the outcomes of the event - if we repeated a probability experiment many times, the expected value will equal the average of the outcomes of the experiment. (e.g. rf(x) dr yields the expected value for a density f(r) with domain on the real numbers.) Find the expected value for one of the valid probability densities above.

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Could you solve this question and put explanation as well please Thank you.