Banner Ad 1

Collapse

Announcement

Collapse
No announcement yet.

please explain ""cumulative distribution function"""

Collapse
X
 
  • Filter
  • Time
  • Show
Clear All
new posts

  • please explain ""cumulative distribution function"""

    please explain ""cumulative distribution function""..what a cdf is ...give a detail explanation..infact i am confused in it..i do have the topic in my book but i am not getting it at par...
    and also please explain the solutions for the following 2 questions related to cdf..

    Q1:it is given that the cdf of a discrete random variable is F(x)=1-(1/2)^x+1 , for x=0,1,2,.... and zero for x<0..
    Find a) P(X=3) b)P(7<=X<10) c) pmf of X

    Q2:the cdf of a r.v is given by
    F(x)=0.25e^x if x<0
    0.5 if 0<=x<1
    1-e^-x if 1<=x

    Find a)P(X=0) b)P(2<X<5) c)P(X<-3) d) P(X<1)

    now please ,dont just answer my questions but give a detailed explanation also because i do have the solutions for the 2 questions but i am not able to understand properly ..
    thanks
    i would really appreciate if sir kriz would answer my queries..

  • #2
    Originally posted by insaan
    please explain ""cumulative distribution function""..what a cdf is ...give a detail explanation..infact i am confused in it..i do have the topic in my book but i am not getting it at par...
    and also please explain the solutions for the following 2 questions related to cdf..

    Q1:it is given that the cdf of a discrete random variable is F(x)=1-(1/2)^x+1 , for x=0,1,2,.... and zero for x<0..
    Find a) P(X=3) b)P(7<=X<10) c) pmf of X

    Q2:the cdf of a r.v is given by
    F(x)=0.25e^x if x<0
    0.5 if 0<=x<1
    1-e^-x if 1<=x

    Find a)P(X=0) b)P(2<X<5) c)P(X<-3) d) P(X<1)

    now please ,dont just answer my questions but give a detailed explanation also because i do have the solutions for the 2 questions but i am not able to understand properly ..
    thanks
    i would really appreciate if sir kriz would answer my queries..
    To start, the cumulative distribution function is defined to be the probability that X less than or equal to x = P(X<=x). For continuous functions, you would integrate the pdf (the density function) to compute the cdf, and for discrete distributions, you would sum the pdf over all possible x.

    So, for question 1, we get that P(X=3) = F(3) - F(2), since F(3) calculates the probability that X is 0, 1, 2 or 3, and F(2) calculates the probability that X is 0, 1 or 2. Subtract the two and you're left with the probability that X=3 --> P(X=3).

    1b) is solved the same way, but pay attention to the inequalities. You want the probability of X being 7, 8 or 9 (but not including 10). So, you want F(9) - F(6) [why is this?].

    For 1c), if you need only the numerical answers, you can do this problem the same way as 1a): that is, P(X=0) = F(0), P(X=1) = F(1) - F(0), ... and so on. Otherwise, you can use f(x) = F'(x), where f(x) is the density, and F'(x) denotes the derivative of the distribution function.

    Comment


    • #3
      Cdf

      Am I "sir kriz"? That's nice, if I am. Thank you. The cumulative distribution function, or CDF, as actuaries like to call it, for a random variable X, is:
      F (x) = Pr (X <= x)

      >Q1:it is given that the cdf of a discrete random variable is F(x)=1-(1/2)^x+1 , for x=0,1,2,.... and zero for x<0..

      You probably mean F(x)=1-(1/2)^(x+1), otherwise the question does not make sense
      So ...
      F(0) = Pr (X <= 0) = 1/2
      F(1) = Pr (X <= 1) = 3/4
      F(2) = Pr (X <= 2) = 7/8
      F(3) = Pr (X <= 3) = 15/16
      etc.

      Find a) Pr(X=3) = F(3) - F(2) = 1/16 (it's this simple only for discrete distributions hitting only integers)

      b)Pr(7<=X<10) = Pr (6 < X <= 9) = F(9) - F(6)

      c) pmf of X
      f(0) = 1/2
      f(1) = 3/4 - 1/2 = 1/4
      f(2) = 7/8 - 3/4 = 1/8

      I am worried though that what you need is not solutions to these, but careful
      reading of a textbook. These are questions from the very beginning of the material covered on exam P. Every probability textbook will cover this. You really need to get such a textbook and read it -- before you do exercises.

      Please read a probability textbook -- what books of such nature do you have access to? Do you have any study manuals for the exam P?

      Yours,
      Krzys'
      Want to know how to pass actuarial exams? Go to: smartURL.it/pass

      Comment


      • #4
        thanks 1st of all for quick reply
        i think i failed to rectify my question
        i have the solution for all these questions...
        i was just pondering at the time of submitting question that why is not
        P(7<=X<10)=F(10)-F(6) ; now if answering this question one might say that this is so because x is less than 10 but not equal to10 so we take F(9) ..and X is greater than 7 but also equal to 7 thus we take F(6) ..this is what my approach and i think so that it is correct because it makes sense
        BUT where i was confused than was that in drawing graphs we consider P(x<=10) = P(X<10) and therefore i thoght that P(x<10)=F(10)
        then why is the discrimination so in general calculations..
        thanks

        AND ONE MORE THING
        I SOLVED YOUR ASM SAMPLE EXAM ..I DONT CONSIDER THAT WELL ENOUGH BECAUSE WHAT YOU DID WAS THAT JUST PUT THE PAST PAPER OF 1992...
        I SOLVED YOUR EXAM .IT WAS EASY AND I SCORED ABOUT 65% (LOW SCORE FOR AN EASY EXAM..I HAVE GOT THE REASON ,,I HAD LEFT A FEW TOPICS UNREAD)
        BUT IF YOU ARE JUST OFFERING SUCH EXAM IN YOUR ASM MANUAL THEN I THINK THAT I NEED NOT BUY YOUR MANUAL AT ALL BECAUSE THE MANUAL I AM USING HAS ALL THE RELEVANT QUESTIONS OF ALMOST ALL THE PAST EXAMS .....
        I AM SORRY IF I AM HARSH AT THE STAGE ..I RESPECT YOU BUT THIS IS WHAT I FEEL.IF YOUR SAMPLE EXAM WOULD REALLY HAVE BEEN A SELF MADE ONE .THEN I WOULD REALLY HAVE APPRECIATED A LOT.BUT CHEERS FOR U.. YOU R GREAT ..BECAUSE YOU HELP EVERYBODY A LOT AND YOU ARE WORKING FOR THE BETTERMENT OF THE STUDENTS
        THANKS

        Comment


        • #5
          Originally posted by insaan
          thanks 1st of all for quick reply
          i think i failed to rectify my question
          i have the solution for all these questions...
          i was just pondering at the time of submitting question that why is not
          P(7<=X<10)=F(10)-F(6) ; now if answering this question one might say that this is so because x is less than 10 but not equal to10 so we take F(9) ..and X is greater than 7 but also equal to 7 thus we take F(6) ..this is what my approach and i think so that it is correct because it makes sense
          BUT where i was confused than was that in drawing graphs we consider P(x<=10) = P(X<10) and therefore i thoght that P(x<10)=F(10)
          then why is the discrimination so in general calculations..
          thanks

          AND ONE MORE THING
          I SOLVED YOUR ASM SAMPLE EXAM ..I DONT CONSIDER THAT WELL ENOUGH BECAUSE WHAT YOU DID WAS THAT JUST PUT THE PAST PAPER OF 1992...
          I SOLVED YOUR EXAM .IT WAS EASY AND I SCORED ABOUT 65% (LOW SCORE FOR AN EASY EXAM..I HAVE GOT THE REASON ,,I HAD LEFT A FEW TOPICS UNREAD)
          BUT IF YOU ARE JUST OFFERING SUCH EXAM IN YOUR ASM MANUAL THEN I THINK THAT I NEED NOT BUY YOUR MANUAL AT ALL BECAUSE THE MANUAL I AM USING HAS ALL THE RELEVANT QUESTIONS OF ALMOST ALL THE PAST EXAMS .....
          I AM SORRY IF I AM HARSH AT THE STAGE ..I RESPECT YOU BUT THIS IS WHAT I FEEL.IF YOUR SAMPLE EXAM WOULD REALLY HAVE BEEN A SELF MADE ONE .THEN I WOULD REALLY HAVE APPRECIATED A LOT.BUT CHEERS FOR U.. YOU R GREAT ..BECAUSE YOU HELP EVERYBODY A LOT AND YOU ARE WORKING FOR THE BETTERMENT OF THE STUDENTS
          THANKS
          The SINGLE best "sample exam" is one comprising past exam questions. There is no better way to get a feel for what these exams are like. These include the old exam 110, and exam 1 tests. Thumbs up to all those who post relevant exam questions.

          This is not an attempt to flame you but when is this exam? Early May? If that is the case you have less than a month left to prepare and you don't know what a c.d.f. is? Have you taken a thorough calculus based statistics class? Again, please don't take this as an insult, I just find it a little intriguing that one of the most basic statistical concepts is giving you trouble with the exam just around the corner.

          Goodluck.

          Comment


          • #6
            Originally posted by insaan
            AND ONE MORE THING
            I SOLVED YOUR ASM SAMPLE EXAM ..I DONT CONSIDER THAT WELL ENOUGH BECAUSE WHAT YOU DID WAS THAT JUST PUT THE PAST PAPER OF 1992...
            I SOLVED YOUR EXAM .IT WAS EASY AND I SCORED ABOUT 65% (LOW SCORE FOR AN EASY EXAM..I HAVE GOT THE REASON ,,I HAD LEFT A FEW TOPICS UNREAD)
            BUT IF YOU ARE JUST OFFERING SUCH EXAM IN YOUR ASM MANUAL THEN I THINK THAT I NEED NOT BUY YOUR MANUAL AT ALL BECAUSE THE MANUAL I AM USING HAS ALL THE RELEVANT QUESTIONS OF ALMOST ALL THE PAST EXAMS .....
            I AM SORRY IF I AM HARSH AT THE STAGE ..I RESPECT YOU BUT THIS IS WHAT I FEEL.IF YOUR SAMPLE EXAM WOULD REALLY HAVE BEEN A SELF MADE ONE .THEN I WOULD REALLY HAVE APPRECIATED A LOT.BUT CHEERS FOR U.. YOU R GREAT ..BECAUSE YOU HELP EVERYBODY A LOT AND YOU ARE WORKING FOR THE BETTERMENT OF THE STUDENTS
            THANKS
            Why should Dr. Ostazsewski create an exam from scratch and distribute it free of charge? That somewhat defeats the purpose of the economics here, no? I think he's made it clear that he is more than capable of explaining Exam P topics (and probably a very similar treatment of other exams, like FM, M and C - coming in the Fall), and I wouldn't doubt that his manual does the same. I would imagine that if his manual didn't explain something well, he would be available to specific questions.

            Comment


            • #7
              ASM sample exam

              Please note that 65% is not enough to pass the test. To assure yourself of passing, you need 70% or better, anything below 70% has some risk of failing, and under 60% will almost certainly fail. So ... this practice exam I posted, that you do not think much of still shows that you need to study, and you can learn what you need to study from areas of questions you missed.

              As for buying my manual, this is, of course, your decision. I believe I have written it in a way that will help you pass the exam. You are obviously free to disagree. One thing I would stress is that studying old exams is a good exam strategy, and you should do as many old exams probability problems as you can. I have written extensively on this in a variety of forums: what you need is a solid mathematical foundation in probability PLUS a lot of practice with old exams. This is what I have put in my manual.

              Yours,
              Krzys'


              Originally posted by insaan
              thanks 1st of all for quick reply
              i think i failed to rectify my question
              i have the solution for all these questions...
              i was just pondering at the time of submitting question that why is not
              P(7<=X<10)=F(10)-F(6) ; now if answering this question one might say that this is so because x is less than 10 but not equal to10 so we take F(9) ..and X is greater than 7 but also equal to 7 thus we take F(6) ..this is what my approach and i think so that it is correct because it makes sense
              BUT where i was confused than was that in drawing graphs we consider P(x<=10) = P(X<10) and therefore i thoght that P(x<10)=F(10)
              then why is the discrimination so in general calculations..
              thanks

              AND ONE MORE THING
              I SOLVED YOUR ASM SAMPLE EXAM ..I DONT CONSIDER THAT WELL ENOUGH BECAUSE WHAT YOU DID WAS THAT JUST PUT THE PAST PAPER OF 1992...
              I SOLVED YOUR EXAM .IT WAS EASY AND I SCORED ABOUT 65% (LOW SCORE FOR AN EASY EXAM..I HAVE GOT THE REASON ,,I HAD LEFT A FEW TOPICS UNREAD)
              BUT IF YOU ARE JUST OFFERING SUCH EXAM IN YOUR ASM MANUAL THEN I THINK THAT I NEED NOT BUY YOUR MANUAL AT ALL BECAUSE THE MANUAL I AM USING HAS ALL THE RELEVANT QUESTIONS OF ALMOST ALL THE PAST EXAMS .....
              I AM SORRY IF I AM HARSH AT THE STAGE ..I RESPECT YOU BUT THIS IS WHAT I FEEL.IF YOUR SAMPLE EXAM WOULD REALLY HAVE BEEN A SELF MADE ONE .THEN I WOULD REALLY HAVE APPRECIATED A LOT.BUT CHEERS FOR U.. YOU R GREAT ..BECAUSE YOU HELP EVERYBODY A LOT AND YOU ARE WORKING FOR THE BETTERMENT OF THE STUDENTS
              THANKS
              Want to know how to pass actuarial exams? Go to: smartURL.it/pass

              Comment


              • #8
                Practice exams

                Thank you for kind words, Wat. Allow me to comment: I would not ever discount the importance of doing old exams problems. There is continuity in the way these exams are, and many problems repeat, if not exactly, then in a basic structure. You should do a lot of problems from old exams. And I encourage you to read the solutions I gave: I am trying to show you efficient solutions, many of them are likely to repeat on the real test. Finally, I am posting exercises in this forum.

                Eventually, when you pass the exams, you will want to obtain employment. I am quite certain that your potential employer would enjoy having you work for no pay. But you might object. You would not mind showing your skills in an interview for free, but eventually you expect to be paid. My sample exam and sample exercises is my interview. Eventually, you will need to decide whether you want to hire me. But if you consistently expect people to deliver services and goods to you without compensation, you are likely to end up getting your money's worth ...

                Yours,
                Krzys'


                Originally posted by wat
                Why should Dr. Ostazsewski create an exam from scratch and distribute it free of charge? That somewhat defeats the purpose of the economics here, no? I think he's made it clear that he is more than capable of explaining Exam P topics (and probably a very similar treatment of other exams, like FM, M and C - coming in the Fall), and I wouldn't doubt that his manual does the same. I would imagine that if his manual didn't explain something well, he would be available to specific questions.
                Want to know how to pass actuarial exams? Go to: smartURL.it/pass

                Comment


                • #9
                  For the record, Dr. O, I probably would've considered picking up your manual for Exam M, had I heard about it earlier.

                  If I don't pass, I'll probably give it a good thought.

                  Comment


                  • #10
                    Originally posted by wat View Post
                    For the record, Dr. O, I probably would've considered picking up your manual for Exam M, had I heard about it earlier.

                    If I don't pass, I'll probably give it a good thought.
                    deleted - spam
                    Last edited by Irish Blues; September 28 2010, 10:18 AM.

                    Comment

                    Working...
                    X