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QUESTION 12Let 0 = {a,b,C,d,e} ad let P be a probability measure on 0 such that P({a})= .2,P({b})= 3,P({c})= .1,P({d}) 25,P({e}) .15. Define the sigma-algebra $ as ...

Question

QUESTION 12Let 0 = {a,b,C,d,e} ad let P be a probability measure on 0 such that P({a})= .2,P({b})= 3,P({c})= .1,P({d}) 25,P({e}) .15. Define the sigma-algebra $ as follows: F ={@,{a,b,c} {a,c,d,e}{a,c} 0,{b,d,e} {b} {d,e}} For the random variable X given by X(a)=X(b)= 2X(c)=X(d)=1,X(e)=3,compute E(X | F) and evaluate this random variaole at W=e.0 2 1.80 70 None ofthe alternatives is correct: 5

QUESTION 12 Let 0 = {a,b,C,d,e} ad let P be a probability measure on 0 such that P({a})= .2,P({b})= 3,P({c})= .1,P({d}) 25,P({e}) .15. Define the sigma-algebra $ as follows: F ={@,{a,b,c} {a,c,d,e}{a,c} 0,{b,d,e} {b} {d,e}} For the random variable X given by X(a)=X(b)= 2X(c)=X(d)=1,X(e)=3,compute E(X | F) and evaluate this random variaole at W=e. 0 2 1.8 0 7 0 None ofthe alternatives is correct: 5



Answers

4-13. Suppose the cumulative distribution function of the random variable $X$ is $$F(x)=\left\{\begin{array}{lr}0 & x<0 \\0.2 x & 0 \leq x<5 \\1 & 5 \leq x\end{array}\right.$$ Determine the following (a) $P(X<2.8)$ (b) $P(X>1.5)$ (c) $P(X<-2)$ (d) $P(X>6)$

You can write S. P of X. The zero Occurrences offering to buy six times. So it is one x 3. 1.5 appearances again to buy six times. Again 1.3 X equals to two is 16 times. It's the So this is one x 6. And Finally there is a operations of x equals 2 3. This combining these all possibilities we get there probably be Frandsen or pdf cruelty density concept. Yeah. Yeah. Mhm. Now for the second part it is asking about some probabilities. So part A P A is already defined X 1.5 years. one x 3. The second part Yeah. Between 0.5 and 2.7. So which values are in 0.5 and 2.7. Do you think the X would be Greater than 0.5 in less than mhm 2.7 These values will be The x equal to 1.5 plus guarantee of X equals two. There's only one x 3. Last one x 6 which is finally three Way 6. So you can say one by two. Yeah. for the part CBX greater than three it will be zero because no occurrences about three P X. Didn't three will be zero. Part B Acts between zero and 2 which will user or create. So it is asking P X Greater than zero and Get an equal to zero in Lesson two. Mm This is including PX zero plus PX 1.52 will not be included because inequality sign it's not on Sunday. So it will be just one x three less, one x 3, which is to work. And the final part is E which is saying the X equals to zero or X equals two BX equal to zero, or X equal to two will be p x zero plus bx two. He extra values one x 6, the f zero values one by three again the submission of both. And you will be one but three x 6. Or finally we can say one bite. So this is our final solution.

Yeah. That's probably been given the sample space of a random experience. Experiment with a further random variable being defined. That's false. Now we want to determine the probability mass function from this. Now we know that each outcome is equally likely from A through F. So since we have six options there that means the probability of A. Is equal to the probability of B. Does include all these probabilities Which is 1 6. Since they were equally likely. Now here on a. We want to find the probability the X. Yeah. Is everyone 1.5. Yeah. Now there are two different values on their where access 1.5 and that's at c. and D. So since each of those is equal to 1/6 I mean this probability is 26 which is one third. So the probability of 1.5 is one third mm On dealing with the probability of being between .5 and 2.7. Now count all the different values Where access between 2.4.5 and 2.7. And there are three of them c. d. and E. And so he and since they're equally likely that means this is 36 Which is one half. And so that probability is 1/2 On C. We want the probability access greater than three And there are no values on that table where actually greater than three. And so that's a probability of zero On the we want the probability access between zero and 2. It can be zero. It cannot be too. And at A B. C. And D we all have those values. And so there are four values Each with a probability of 1 6. And so this is 46 Which is 2/3. And then lastly on E We want the probability at zero or that's us too. Mhm. And there are three different values for X0 or two. And so this is 36 which gives us the probability of one half.

No. Here we help piece vice function. So for negative would do for or function is model. It's X divided by 10. And for that interval for fax is a googol Zeros. Now consider this thing's on Mardi Les function so he are more model A sex is it will do Negative x When nexus between Kuku Siegel and more delay Sex is a photo for the two eggs When exes between cool Asadi zero group for No I mean really used you and right in the regional accent Do now put the radio Thanks a lot here more populous X divided by 10 here now our intern release negative too negative group for So I used this underworld. So for negated to zero, our function is minus x So here for negative too little Oh, are functioning minus eight And for zero before from Sonny's ex Soviet for zero before function ese Thanks. No, you're one by Danny's constant. So they get outside And here the negative sign toe here Harry and they get you saying Xing to exceeds X square. I mean here except to exceed experience integration off X squared is extremely worried by three. I've been here X cubed, divided by three and exhibit a couple. You make minus lower limit massively. Where these we get music Or do we get by bean, which is our office in de sorts? In these correct answer. Thank you.

So here, Questioning 23. We don't need you functioning for fax. Now, as you can see here we have more sex. So make the graph. Now, as we can see here, more duo sex is equal to minus X for my ass to go Siegel And the more you know sex physically go X when access lies with me Seed or cool four. So can right here More delis. Nexus is a point minus x Texas last between getting Coop Siegel and more doula Sex is a composite directs My ex is life's dream Ciro Before now the second thing is to find expected with your meal is doing boy. And to the thanks. Yes, No Bailey off. Thanks. So are here. Which is more do sex curated by den. Now you're more beautiful. Sex is a Borgia minus x on the interweb c Cool. Sorry, Minister received, you know, minus to come. See you on more delis. X is equal Durex for seed or group four. Okay, so your ex into exceeds expert in right negative sign Here, International, Your ex queries It's cubed you edited by teen deviation Next body being X cube. You ready by now? is that you don't believe it. But you see, Roque, you do it on three minus my most true destroyed two divided by three Been your ex. Opportunities for your fork You directed by three minus divided by three. Your music would remember this one time C o que ceo loss through a list with reason for strategic Buried by 3 64 Really? But you've been here zero movies, seal on by some people. These we get O R. Probably. Sorry. Expected. William, you lease 2080. Ready by Dean. Jeez up, Sandy. Thank you.


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