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Find E(X) for the random variable X whose cdf is given by:0 b < | 4 1<b < 2 4 2 <b < 4 1, b 2 4F(b)...

Question

Find E(X) for the random variable X whose cdf is given by:0 b < | 4 1<b < 2 4 2 <b < 4 1, b 2 4F(b)

Find E(X) for the random variable X whose cdf is given by: 0 b < | 4 1<b < 2 4 2 <b < 4 1, b 2 4 F(b)



Answers

A PDF for a continuous random variable $X$ is given. Use the PDF to find (a) $P(X \geq 2),(b) E(X),$ and $(c)$ the CDF. $$f(x)=\left\{\begin{array}{ll}\frac{3}{64} x^{2}(4-x), & \text { if } 0 \leq x \leq 4 \\0, & \text { otherwise }\end{array}\right.$$

The probability that this rendering variable is greater than or equal to two. He calls the anti girlfriend 2 to 4. And the probability density function, which equals miners or three arts. And for all 2 to 4. And the probability is 1 3rd The expectation, because the energy go from 0 to 4. Eric's times the probability density function Richie calls. Well, that's great log ax problem 124 It's 1:00. And this echoes 43 long for Which is approximately 1.8. Fuck the humanity of distribution function Vehicles into you go from 1 to X. And the probability density function where'd she calls Miners Forward three T From 12 ounce as a Chelsea cole's boy, X minus full 43 arts.

In discussion will recall that if the function F x is the BDF doesn't realize lender in the girl from minus infinity to infinity on the function f x to the ANC's we could you one in discussion here were given the function that function f X equal which in the for expert minus five and were given that X here will be valid Found the interval from one up to infinity. Now let's try Thio verify But I that the FX will be the density So we need to compute in the girl from one to infinity I'm the fall expel minus five the X Then we get Nico to anti derivative this Juanico to the four times he will have the expel minus four other minus four evaluated from going to infinity Everyone the infinity inside we will Garnick agenda is zero on then falcons and the one fund will be the man is gonna be plus here Then we have one bel minus far and story go to the one so doesn't implies that the function F X is a pdf for all X Greater ego to the one and then for the party here we want to fight the cumulative distribution function. So the F comes on the X. It's a nickel to the integral from one to the eggs. Here I'm the function. Then stay here. Well, before we changed the X to the three by minus five the D then until the river the Amazon echo to the minus. X Bauman is far if at the here Sorry, evaluated from going thio X then we get equal to hear you get equal to the minus one of the expo four plus you have one or we can register into the one minus one of the expo far. So this will be the cumulative function for X in interval from one to infinity. Now find a bus C Once you use the F X, Did you find a probability that the X is between interval from 1 to 2 and then which is equal to the F capital in the Tu minus F Captain, the one we're going to go to one minus one over to before minus one, minus one. Number one. Before that, we get Nico, too. There's only have one minutes one of the 16 Rico to the, uh 15, number 16 minus this one. Echo to the zero. So again, exactly. Coaching of 15/16. Now the probability in donde x greater ego to do so, it will be equal to the F on the infinity, minus f from the Jew. So get equal to have infinity in global Inside the of infinity, You get equal to the one minus now. Evan, with you, we get equal to the one minus one over to power of far. So again, decode you one minus one will be zero, and then we have the one off the 16. So that's gonna be the answer for the past. See here.

In this question, we're recording that if we have the random variable X has the cumulative distribution function, F comes from the X that we can find the probability that the XB trained in for from hp its unique culture The air from the bay on a F on the A it is question here were given, uh, distribution F X. They go to the X minus one about Jew for the X on the interval from one to do and we need to find a B. Since that we have the probability that the exhale smaller equal to the be it will be equal to no one over far. Notice that we can insert this under lower power for the X will be the starting point will be the one and they found the left hand side here We can really stand to the from the B minus the f from the one because you want off a far Now, however, the B we get equal to the B minus one square miners everyone equal to the one minus one squared equal to one of the far are we get now B minus one squared equal to one of the far. And it means that the B minus one equal to plus the miners one of the two. And then from here we can get a be equal to one present manners one half on the B. We equal to the it will use. The plus will be in the three and two and it will use the miners. We have half. So have to values on the B. Now in this question, yeah.

In this question would you conduct if the random variable X has the community distribution function F X here on, then we can find a probability. Donde Thanks. Me too. In the interval, I n b actually go to the from the B minus and from the I in this question here were given the distribution run Better vision function F X. You go to the one of a far X square for the accident interval from 0 to 2. And in this question, they're asking that you find a be sustained. The probability that the ex model continue be it will be continues upon Zo nine here they were blind of formula here we can we're understanding tune the I have from the B here we don't know yet. Minus here we see that the right and bond equal to the zero here. So we re minus from the zero So again ico too. Here we have the This will be the distribution distribution function. So getting close to one of the four b square minus Arabs are equal to the one of the farther square and we want this one equal to the job on 09 now what you saw this one again. It means that we have the one off is quite equities upon his own nine. And this means that the peace quiet, echo Jew as upon his own nine times four get nickel Jews upon 36 doesn't implies Then the big will be equal Jew the plus Amanda Square it in is about 26. Then we get equal Jew. The plus a man is upon six on because X is in the monster in the world. Therefore, we will reject the miners here. Then we were equal to the 0.6 and that's really the answer for this question.


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