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Let F(x) is probability distribution function of continuous random ~2x variable X and If F(x)= 2e X > 0 to other wise Then P( Is x < 3)Select one (e-2 ~e-6...

Question

Let F(x) is probability distribution function of continuous random ~2x variable X and If F(x)= 2e X > 0 to other wise Then P( Is x < 3)Select one (e-2 ~e-6) 2(e-1 _ e-3) (e-3 ~e-1) (e-1 + e-3)

Let F(x) is probability distribution function of continuous random ~2x variable X and If F(x)= 2e X > 0 to other wise Then P( Is x < 3) Select one (e-2 ~e-6) 2(e-1 _ e-3) (e-3 ~e-1) (e-1 + e-3)



Answers

Let $X$ be a continuous random variable with the density function $f(x)=2(x+1)^{-3}, x \geq 0.$
(a) Verify that $f(x)$ is a probability density function for $x \geq 0.$
(b) Find the cumulative distribution function for $X.$
(c) Compute $\operatorname{Pr}(1 \leq X \leq 2)$ and $\operatorname{Pr}(3 \leq X).$

So that given a function that ISS a perfect, that she continues probability function that it's equals toe Unter. And it's a station that it calls wanted and restricted from the interval bonus question it calls Toe X and less than or equals toe or so we have to determine the probability three X is greater done. Three hops so you can see this. This is the wrap off shaded portion we're in. This is three hops and restricted toe upper limit the discussion for from this area we can conclude that that place up this is about four minus three hubs times the height hard up probability can probability distribution that work also entered. So we have port minus 1.5. That single stood 2.5 over three are the EPA or it's giving it a purpose limits. Born instable probability will will be equal to the area off 3.2 x call sport and then so 2.5. But about three about she 2.837 So this one is Sequels to see the point 83 and this one, Mr Answer. So this is the description of dysfunction expressed greater than three bottle That will be from to the point to hear toe pork. Because this is the limit is restricted. Function off continues probability.

He is clear. Someone new right here. So we have to satisfy three conditions. The 1st 1 is that the function is continuous seances, a polynomial function. It is true. The 2nd 1 is that the function is non negative. We see that from F zero is equal to zero and half of one is equal to we have. So this is increasing. So it's true. The 3rd 1 ISS that into girl over the interval is equal to one. You see that from 0 to 1 three house thanks comes to minus X t X. This is equal to one, so the three conditions are met. So yes, this is a probability density function. When we calculate the probability, it's from excess less than 0.5, which becomes equal to the integral from 0 to 5. Three Have X times two minus X t x. This becomes equal to three halves from 2.52 x minus square DX, which is equal to three husbands Times Square, minus one that had 1/3 ex cube from zero 25 which is equal to 0.3125

He was clear. So when you married here. So we need to satisfy three conditions. The 1st 1 being the function is continuous, which is true. The 2nd 1 is the function is non negative, which is true. The 3rd 1 the integral off The function on the interval is equal to one. When we calculate it, we go from zero to infinity of x e the negative X t x, which is equal to the limit as a approaches infinity from zero to a exceeds the negative X T x, which becomes equal to the limit of a approaches Infinity Her negative X minus one times E to the negative X from zero to a which is equal to the limit approaches infinity for negative A minus one over each the A plus one. So when we use the l H rule does this equal to one. So yes, this is a probability density function. When we find the probability he goes from one 23 included. So this becomes equal to the integral from 1 to 3 x Eat the negative x t x, which becomes equal to negative X minus one he to the negative x from 1 to 3, which is around 0.537

Writers of this function after backs is a probability density function, not two things to show. 1st 1 is to show that half of axe is known active function, which means that whoever axes always screwed What zero The second wise to show. Ah, the intuition of Apple Ax from me Finch from negative infinity to infinity. He's the one all the time. So the first time he's straightforward because half of acts by the question he's came in by 30 times. Tomorrow, too. Temps 11 is actually true because we know that sort of function. Ax squared on the worldwide stock squared their old group, which means this whole function is good. And for the 2nd 1 to take the intuition off cracks because off of axe is known. 01 axes between your on the one. So this intuition is actually So you sure this is one. Do we say that this function you harbor case it's just the integration of from 0 to 1 off of X Jax, for you can think of Accent piece was function, except that the only number he repeats it this Kovacs and one access be young, one and small and sort of half of actions you. So to do that, that's how I'm going to write down Oakland. Short time for Maxie, another form so cool I'm going to expand or the bracket outside. So after Barrett is 30 two times one minus tracks, plus Jax, which is so because of the thirties, a skater, we can't simply bring this killer outside past two apart. Two times one is absolute You. I was about two times minus tracks. Is my chick cute tracks Cubed and Puss? Actually, no. Next to her four jacks or so, in order to do, these institutions will have to remember one of the formers, which is the introduction of backstory. Detox. This is the one over and puzzling looks forward. That's what space here. That's a costume, they said. The former eaten the first course off tacklers, and this is true and it's not mine. How'd you get this? Formerly we could just show that to this year's 38 times. Big package one word two plus one, which of three angst took asked for free Wyness Blur word concerning this powerful here, So I just went over four plus one, actually, four plus 10 I guess this is just five times actually fight and minus to tower because this to scale around, we bring down this power free and she's three or four because it's possible. And we're going to evaluate these function for Missouri one. Let me say that one actually zeroed in the actually Zordon, this whole from crazier So we don't really care about the doctor. First term is wax. What if you use your calculator or something that you will see that this accident like this turn me the pig bracket? That just someone over 30 30? And this is what is what what? What we want handful party to show it to find the property. What ax? It's more equal to 1/3 again because we just showed up of axes are probably it is their functions off this. It's simply the integration from zero to through backs. Hey, guys, Hogan. This time this here we used zero is because we really care about the values with access smaller than zero, because by the definition of a vaccine, 01 actor smaller than you. So this by our a calculation in party issue, simply 1/3 of that's cute course of fear. So next five minus sure for time. Zach, start to the four. Sorry, very integrating sort of where you want me to. This function from zero for 1/3. And now similarity ends before we actually zero buzz dysfunction. 80 However active throw just substitute, actually 30 dysfunction. What was 30 times the third to be terms off? Third to the power of three. Closer, fierce terms of third to part five, minus half shore forts off himself. Third, two out of four. I would say that this comes to 17 or anyone.


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