The Error Involved in Making a Certain Measurement is a Continuous Rv X With Pdf
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The error involved in making a certain measurement is a continuous rv X with the following pdf. f(x) = 0.09375(4 − x2) −2 ≤ x ≤ 2 0 otherwise (a) Sketch the graph of f(x). (b) Compute P(X > 0). (c) Compute P(−1 < X < 1). (Enter your answer to four decimal places.) (d) Compute P(X < −1.1 or X > 1.1). (Round your answer to four decimal places.)
Related Question
The error involved in making certain measurement is continuous rv X with the following pdf: f(x) 0.09375(4 X) ~2 $* < 2 otherwise (a) Sketch the graph of f{x)_ f(x) 0.61 f(x) 0.4 0.4 0.4 03 03 -3 -3 Compute P(X > 0)- Compute P(-1 < X < 1). (Enter your answer to four decimal places. Compute P(X -1,1 Or X > 1.1). (Round your answer to four decimal places,
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Video Transcript
Hi, I'm David. And I'm in your question. Now let me bring up your question here in the question. Here we are given the density of the random variable X. And here in the question I asked him to choose the right graph from the function F. X. Now to choose the right one. We see that the exhale will be valued between the -2 and two. And it's also Correent for all four options here. So we cannot based on the ranch and domain. Now we will check uh f on the zero means that when X equal to zero, we get equal to the 0.9 3 75 times in the farmer zero square. And it will compare and we have reserved in zone 93 75 times within the far They will get equal to the 0.375. And with this value here we see the right one. We can eliminate this option and we can eliminate this option So it can be eaten first on the 3rd 1. And we see the difference between them, it will be the F. X. And then this could be the 01375 years and also will be eliminated because it's smaller than the 013. So they found the right one must be this option. And that's done for the question. I question be I will compute the probability of the exc residential not to stand the probability to equal to the area under the curve and noticed that it will consider the whole area here, It was exactly equal to one. And we're interested in expert hands also will be half on the area because of the symmetry this half here will be the same as the half on the left. So this means that this area here, it will equal to 0.5. So therefore the answer, he must mean that 0.5 for the B for the C. Once you find the probability X between the minus one and one, so minus one will be here And one will be here. So therefore the probability we're looking for will be the area in the middle. So let me remove this 15 fast and then to find the area in the middle. Notice that we just do this one by the integral but notice that the area on the half on the left will be the same as the half on the right. So that far we can find this probability but taking the integral from zero up to the one but we will multiply this one by two because that would be the same as the one on the left. And then we will have the density will be the 0.0 point 093 75. Times in the four minus X square from the X. So we will bring the 0.93 75. Outside times of the jew someone's so nice. 3 75. We get equal to we're producing outside multiply window to we get equal to the zero coupon one a 75. Now the inside the anti the Riverdale from the four equal to the four X. Untidy. Riverdale on the X squared equals do the expo 3/3 And then eventually from the 0-1. Then we get encroaches upon one and 75 it would be like the one inside we have the 4 -1 out of three. It will break the zero inside 1-0. Therefore we get this one equal to thames with the four minus 1/3. Then we get equal to the 0.68 75. And that's gonna be the answer for the question c zero point six A 75. Now for the question they want to find the probability that X now will be smaller than the -1.1. So let me remove this one. Now The -1.1 will be here and then we want to make it on the left tail and it will be on the right tail. And because of the symmetry this area here will be the same as this area. So they found this one technical to the two times one on the area and choose the one on the right now. So this one will be from the 1.1 to the two. So I will have from 1.1 to the two that we have reserved one. Zone nine 3 75 times and of four minus X, Squire. And then the X. Again it moves on outside and multiply by two. Again equal to the 0.18 75 anti derivative equal to the four X minus the expo three. Number three. Now we will value from the 1.1 to the two. So if we look in the value we get equal to 71 a 75 and it will put a jew inside, we will have the four times two minus the eight out of three. Here we go to the 16/3 minus it will put 1.1 inside. We have four times 1.1 -1.1 Power three divided by three. Then we got equal to that three Born Night 56. So it will compute this one get equal june 16/3 minus the answer, Tamsin. Has anyone won a 75? And then we get equal to the Dessert 1- five. So how many less more energy around here when we found the Small places 2. 82. And that will be the answer for the questions. The they are born to 582. And that's gonna be the answer for this question
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