The diameter of a particle of contamination (in millimeters) is modeled with the probability density function ????(????)=2/????3for ????>1.Determine the following: a.????(????<2) b.????(????>5) c.????(4<????<8) d.????(????<4????????????>8) e. ????such that ????(????<????)=0.95

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Hi, I'm David. And I'm here to have your answering your question. Now let me bring up your question here in the question. Going to discuss about the cantinas random variable with the probability density function. Now, with this F X ego. To the to the X. Power three for the X greater than one. We should be able to obtain the community distribution capital F X. Each equal to the probability theme. The X smaller equal to the small X. The formula technical integral X. Starting from the one up to the volume the X. Then two of the Expo three DX. Then then the untimely ripped from the export of ministry could be expelled from the minus to the venue by minus two. And then environment from one to X. We see that to cancel on the two and then we will have equal to the minus. So it will be one minus no one of the X square. And therefore we have to come to F X. They were equal to one minus one of X square for the X greater than one. Now, the reason why we compute a cumulative distribution function because it would be easier for us to compute the question A to E. Now for the question I want to find the probability I'm the ex model than to for the continuous random variable the equal or not equal would be the same thing. And then this one exactly go to the F on the two, You could look in the value, we have the 1 -1 of the two square, Which is equal to one. Another 1 -1/4 equal to the three other four. For the question be When you find a probability x greater than five again by the compliment is equal to one minus. Probably put it in the next morning equal to five and recognized that it would be the f. Capital of the five Were booking engine Kanda 1 -1 of the five square. Then we get equal to the one h 25. But the question c once you find the probability on the X between the four and the eight we can divide this probability to be the probability of the ex model and eight minus probability on the X. Marks equal to the far again equal or not equal will be the same thing. So which can be equal for the eight here. And we can recognize this one will be the capital m from the eight minus F. Coming to arm the fall And then we get equal to 1 -1 of a square minus The 1 -1/4 square one. Councilor window one. So we have 1/16 -1/84. Then we get equal to -1/64. It goes to the 3/64. Now I found a question be once you find the probability of the X more than four uh X greater than eight because they are destroyed. And so we can register probably pretty ex model and far plus Probably the X. greater than eight. No ex president ford will be the F. On the far President. I will be the 1- probably within the F- eight. And then we have someone -1 other. We can do this would be much easier because we take the complement of the A. I'm the very sexy So we have 1- probably bring him the X. Between the four and 8. And then we have the answer for the city will be 1 -3 out of 64. And then we have the 61/64. Now for the E once you find out Small X. system this problem with the equal to 95. And now this one exactly equal to the air from the small X. equal to the reserve on 95 And F. X. We know equal to the 1 -1 over X. Squire. Equity is about 95. From here. One over x squared will equal to 1 -95. Equal to 0.05. They found the X squared equal to 1/0 0.5. It will be equal to because you're 1 to 5. Echo ju 20. Therefore X. It will be pleasant manners maybe because X here greater than one. So X. Must be equal to the square root on the 20. And this will be the answer from the E. The answer for the D. For the sea. For the B. and for the Eye.

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