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Problem 1 [You can solve this problem nOW Let X,Y : S _ R be two (real-valued) continons random variables with joint pdfif 0 < y < 1 and - y < 1 < y els...

Question

Problem 1 [You can solve this problem nOW Let X,Y : S _ R be two (real-valued) continons random variables with joint pdfif 0 < y < 1 and - y < 1 < y elsefex;x) (T,y) =Calcnlate EIXYI; EIXI, and ElY|: Does ElXY| = Elx] - ElY hold? Are X and Y independent?Problem 2You can solve this problem after we discussed section 5.3 For € NJ let X X, S + Rbe either n discrete random variables with joint pmf P(XI T14 Xn Tn) OT n continons random variables with joint pdf f(t1; Tn )Furthermore; le

Problem 1 [You can solve this problem nOW Let X,Y : S _ R be two (real-valued) continons random variables with joint pdf if 0 < y < 1 and - y < 1 < y else fex;x) (T,y) = Calcnlate EIXYI; EIXI, and ElY|: Does ElXY| = Elx] - ElY hold? Are X and Y independent? Problem 2 You can solve this problem after we discussed section 5.3 For € NJ let X X, S + Rbe either n discrete random variables with joint pmf P(XI T14 Xn Tn) OT n continons random variables with joint pdf f(t1; Tn ) Furthermore; let Q1, - Gn € R_ Show that in either case (i.e_ for discrete RVs on the one hand and for continons RVs on the other hand) , Ea;] a;EIX;] j=[ Now assume that Xn- Xn are in addition independent. Show that in either case (i.e. for discrete RVs on the one hand and for continous RVs on the other hand) , E[X X] = EIXi] EIX,]



Answers

Q1. Given the CDF of a continuous random variable, which of the following processes allows you to get the PDF of that random variable?

1. You Cannot recover the PDF knowing only the CDF
2. Integrate from 0 to 1
3. Integrate over the relevant region
4. Take the derivatives of the CDF

Hi I'm David and I'm here helping you answering your question. So let me bring up your question now. Okay. And now in this question when we discuss about the B. D. F. Of the function and were given the function F. X. X. Over two. Okay we understand. Is that correct? Will be one armor to power X. And we have the access go to 12 and three and then we go to zero otherwise. So here we're going to find a balance on the guy. Notice that the submission of the probability on the X. Echo two I for volume the I must echo to exactly what you want. So let me try to find the probability of the extra co 21 1st. So it changes that we go to the K And then one hour to power one and exactly it got you. OK Times one of it you and now when the probability X equal to two who have gay times one over to our two and we get equal to K. Times one over far and the last one probability exited three. Get negative. Okay times one over to our three. And we get to go to the gate terms 1 # eight now and we want to lie that we end them up. So toto you need to compute the sum here. So when we end them up we see the cable with a common factor inside. We have one of the two plus one of the four plus one of eight. And if we compare this one we'll have 1/2 +14 plus one of eight. We get equal to the seven out of eight. And we want this one exactly echo to one. So it means that came as Echo to the eight out of seven and this will be the value we are looking for.

I am David. And I'm here to have you answering your question. Now let me bring up your question here in this question. We will reveal about the total probability. Reckon Yoda if we have the total probability for any X. It must echo to exactly will be one. So in this question were given the F. X. Echo to pay. Looks like we have to try and then times X. I'm not sure about this. So I will assume that. And now ex every co 212 and three. So let's try to make a table. I'm the probability now. So actually 212 and three now they're probably to get the one we put the one inside here and then we have will be 12 K. And found the probability to get a jew from the act we wanted to hear and I got a 25 day And the last one it will be three in San Ghana 36 gay. And remember that we end up everything that thought probability. There we go. To the 12 game plus 24 game plus 36 K. Exactly equal to one. So if we simplify this one we have the 12 plus 25 36 equals 72 K. Equal to one. Listen tells us that the K. Equity one number 72 that's gonna be the case. We're looking for

Hi, I'm David and I'm here. You have your answering your question. Let me bring up your question here discussion we discussed about the two concept. The first one we went the cumulative distribution function. The second one will be the probability density function. Now we continue that the C T F. He noted that the capital F X and he still the probability that the cup, the random variable X smaller echo in the small X. And then to compute the B T F did not invite a small act from the C D F. So what you need to do the derivative of the K c D F. And then when we do the derivative we should obtained, uh probably did and stay functioning. And when you go back to your question here, which I'm defining processes allow you to get the B D f, I'm the random variable. So we see only the phone will be the right one because take the derivative of the CTF. So that would be the answer.

Hello. So today I'm going to answer the question about cumulative distribution functions. How to pass through a pdf for doing so the only one instruction will be the fourth that is to take a delegate and just want to give you a quick okay Yeah. A Creation Altes answered that you have to deactivate when the priorities a continuous case when it's discreet you have to subtract from each level. So Just to give you a quick understanding, the cumulative distribution function give you what are the values accumulated from 0-1. So normally It's like that where here is zero one and here is zero and you want to do relate to know the levels and in case that is discreet, you just want to have the right in between. You will be X. That is the priority. That it's a month until the next level. So it uses a quick reminder remember that for finding the pdf with the cumulative distribution function you can deactivate but this is only valid when you have the continuous continuous case. If it's not the case if it's discreet you just have to subscribe from each level. I hope the explanation was clear and thank you very much for your time


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