So this particular problem, you've been given the conditions for the CDF off w So for the party, eh? You know that W is our non zero value. So therefore I concede that w was credit and only Puerto zero on duh in a non zero for this part. So therefore, for w less than zero the CDF off W we can write it as B or for capital of Lula's Annie Woodrow the small right w which cannot about it and as a CD off, off, off, off, doubling on duh that. But we need to simplify for different values now. So first I'm going to find reliability for W is equal with zero right into the first part of your wonder find So to find out probably W is equal to zero. The condition going in The question is that it is vey lesson. Is he really? It's between that distribute indignant from zero to me D and for the extension distribution, the value off effects is land on to eat is to minus lambda X, the X So if you apply the intimidation, this is Lambda is to mine is Land X a born minus lambda limiters from zero to Edie. So Lamda is cancelled on if I substitute the limits and get one minus is too minus lambda we be. So this is the Obama team and our music will do zero now. Next is I'm supposed to find the probability when, uh, the capital w well, I between the value zero and a small w Okay, so to start of it, that's what the conditions that are given in the question this we can write is equal probability. Off zero is less than capital W for this condition is K and will be minus video and less than the small value. Doubly So Now we can read out this part like this where we begin mother, black teens I really and then divide for by key. So the expression I don't know that we have zero less than we have gave me. Minus kennedy is less than w. Okay, so then further if I divide toward by key Ah, What we will have here is zero less than the minus. VD is less than w by K. Okay. And for them to add told with VD, Sylvia probability off really is less than the his less than this is W plus we have. Ah, I mean, this would be w by K plus Weedy. Okay, so now are based on this condition we have to integrate from VD toe. This is the blue place DVD upon. Okay. For the whole a lambda it is to mine. Islam dy ex d x. So if I continue with the indication I want to keep from the hazardous dilation is ears to mine. Islam decks upon. Minus lambda limits are from TD to Mrs W. Place Cady upon Cape. So Amanda gets cancel your and the value of an expression that we get now is, uh it is to my nest DVD. I'm sorry. This is Edie's to minus not Katie, land of VD and, uh, minus. We will have e j screw minus. I don't know, bless gave me the bike. So this was for the conditions between zero and part of you. Now we're talking about ah, the values for no w s president or equal to zero. Then, in this case, the CDF is they find us again. If off w will be re off w les and equal w So this part I can take this as POWs, zeal plus the value off between the Oran. Smart. Lovely. So we found what the values if I substitute surely one minus CDs to mine Islam W t plus, this is years to minus Lambda. Really minus. It is to minus the group less giving the of wonky, so you can see if we can save this park. So what remains is one minus is to minus new place gave India punky. So based on this, I can therefore conclude the CDF as a form W Can we return here as eagled for st abuse lessons, you know? And this is one minus beatings to minus the blue bliss que vd by G for double Ingrid and zero. Now we want to the part B. They're also trying to find the pdf for this particular part. So the pdf off, uh, W for w Great as you will be. Ah, form W We can take this as dead over two off the CDF. So finding the dead emitter off this expression with double is one minus easiest minus lambda. We have the blue bless que vd of one key. What's yours if I differentiated B minus off, please to minus Lambda into this w place DVD bikey on into the Internet of Atonement. Don't move me! Minus lambda by key to the final value for the sun Get in. Here it is Lambda by key in tow. Edie's to minus lambda W S K V d Bike key. So this is the pdf for Dylan particular part. Now we also know that and I lose a mixed distribution. So I can say that since W is mixed distribution eyes getting the question with the combination of discrete and continuous boat, it's now to find out the expectation for W uh when he was a concept off the street as a list continues. So then we're going to write expectation of W So for discreet, I'm gonna take this as X into the office. So Lazio and be off W is equal to zero. And for this partisanly continue. So you haven't gigolos Theo to infinity be w in tow, F w Theo into the blue. We've just found out. So that's actually Lambda my gay and oh, we have evens to minus lambda and this is w by gay plus really with need of you so I'm gonna get a lambda by gay Healy's tow. Give my understanding the racket. We have mine Islam, WD questions digging that part outside healed and in bigger list for the organ firmly between w ant eaters to minus lambda w by key. I don't know. So, uh, I blame the indignation by parts. Now what the hell are you going to get the blue in tow? Indignation for this is he is to mine, Islam. That of you by k upon my name is Linda by giving them a tron zero to infinity minus is integral zero to infinity, the inevitable that we will be one and again, indeed, Asian off eBay stores derided by Mayan Islam that w born gay, sodium to move this w sure really dealing with that. So Lamda McGee is a constant and quit Needham. So for that, huh? If you take my Islam DeBakey comment well too well, have minus okay by land Outside will get cancelled on dhe. We will have Edie's to mine Islam Davidi as just on in the bracket here, the parliament. This will change to zero because it just reminds and pretty zero and W Walter white hunters use the force. Thomas is you know directly. This would change to Plus, we have here on Lander. I'm keeping London. Keep your eyes off now because that I could cancel anyway. And for this they are hindering in delusion. So you can have years to minus lambda doubling by key upon mine is lambda by P. Yodo Infinite. So I can gather this year on. And now, after putting the limits, the Lambda by K it is true minus lambda VD and the Parliament is to minus. Infinity is zero and mine is he? This was you. Is one Ondas divided by minus one minus one gets cancels on. Duh. There is a connection of yours. Just doesn't cancel into frankly can want apply. So his land on my key. And do I have key square by land a square and the nominee elements, he'll have one minus zero social. Now, simply for this part. The final answer for the execution of doubling that I'm getting is give our land up years to minus lander VD. So this is the final answer for expectation off W