Results are out! Find what you need...fast. Get quick advice or join the chat
Hey! Sign in to get help with your study questionsNew here? Join for free to post

S1 Help - Cumulative distribution function

Announcements Posted on
Applying to uni this year? Check out our new personal statement advice hub 28-11-2014
    • Thread Starter
    • 1 follower
    Offline

    ReputationRep:
    Hi there,

    Just a quick question, I am slightly confused as to the mark scheme for this question:

    (b) The continuous random variable Y takes values between 1 and 2 and its cumulative distribution function F is given, for 1 < y < 2, by
    F(y ) = ay + by^2.
    Find the values of the constants a and b.

    Now I understand to input F(1) into it so I get a+b=0 (like what the mark scheme says) and then F(2) so 2a+4b.. but then it equals this second equation to 1 for some reason?

    I know how to find a and b after getting the two equations but I just wanted to know why that second equation equals 1?
    • 46 followers
    Offline

    ReputationRep:
    (Original post by Ryan44)
    Hi there,

    Just a quick question, I am slightly confused as to the mark scheme for this question:

    (b) The continuous random variable Y takes values between 1 and 2 and its cumulative distribution function F is given, for 1 < y < 2, by
    F(y ) = ay + by^2.
    Find the values of the constants a and b.

    Now I understand to input F(1) into it so I get a+b=0 (like what the mark scheme says) and then F(2) so 2a+4b.. but then it equals this second equation to 1 for some reason?

    I know how to find a and b after getting the two equations but I just wanted to know why that second equation equals 1?
     F(y) represents the cumulative distribution function, its range is given as  0 &lt; y &lt;  1

    So to solve we know that at the lowest point of range,  F(1) = 0 , and at the highest point,  F(2) = 1

    The  1 represents the total probability(the total area under the p.d.f graph)
    • Thread Starter
    • 1 follower
    Offline

    ReputationRep:
    (Original post by raheem94)
     F(y) represents the cumulative distribution function, its range is given as  0 &lt; y &lt;  1

    So to solve we know that at the lowest point of range,  F(1) = 0 , and at the highest point,  F(2) = 1

    The  1 represents the total probability(the total area under the p.d.f graph)
    So does F(y) always have a range of 0 < y < 1?

    Thanks for your answer!
    • 46 followers
    Offline

    ReputationRep:
    (Original post by Ryan44)
    So does F(y) always have a range of 0 < y < 1?

    Thanks for your answer!
    No, it depends upon the question.

    Example:
    It  F(y) has a range of  2 &lt; y &lt; 5 . Then  F(2)=0 \ and \ F(5)=1
    • Thread Starter
    • 1 follower
    Offline

    ReputationRep:
    (Original post by raheem94)
    No, it depends upon the question.

    Example:
    It  F(y) has a range of  2 &lt; y &lt; 5 . Then  F(2)=0 \ and \ F(5)=1
    I see what you mean as in my question it is between 1 < y < 2 and that F(1)=0 and F(2)=1

    But does the F(higher boundary) always equal to 1 and the F(lower boundary) always = to 0?
    • 46 followers
    Offline

    ReputationRep:
    (Original post by Ryan44)
    I see what you mean as in my question it is between 1 < y < 2 and that F(1)=0 and F(2)=1

    But does the F(higher boundary) always equal to 1 and the F(lower boundary) always = to 0?
    Yes.

    Do you understand what does F(y) actually represent?

    Do you know the difference between  f(y) \ and \ F(y) \ ?
    • Thread Starter
    • 1 follower
    Offline

    ReputationRep:
    (Original post by raheem94)
    Yes.

    Do you understand what does F(y) actually represent?

    Do you know the difference between  f(y) \ and \ F(y) \ ?
    Couldn't give you the definition between the two although I know how to convert f(y) to F(y) and vice versa correctly.

    f(y) to F(y) you integrate? and F(y) to f(y) you differentiate the function?
    • 46 followers
    Offline

    ReputationRep:
    (Original post by Ryan44)
    Couldn't give you the definition between the two although I know how to convert f(y) to F(y) and vice versa correctly.

    f(y) to F(y) you integrate? and F(y) to f(y) you differentiate the function?
    Yes, you are correct. I thought that you might be misunderstanding them.

    We know the total area under the  f(y) curve is 1, so if its range is  0 &lt; y &lt; 3
    Then the total area is  \displaystyle \int ^3 _0 f(y) \ dy = 1 = F(3)

    Hope it makes sense.

Reply

Submit reply

Register

Thanks for posting! You just need to create an account in order to submit the post
  1. this can't be left blank
    that username has been taken, please choose another Forgotten your password?
  2. this can't be left blank
    this email is already registered. Forgotten your password?
  3. this can't be left blank

    6 characters or longer with both numbers and letters is safer

  4. this can't be left empty
    your full birthday is required
  1. By joining you agree to our Ts and Cs, privacy policy and site rules

  2. Slide to join now Processing…

Updated: May 31, 2012
New on TSR

Vote for your favourite Christmas film

Win a bundle of Xmas DVDs

Article updates
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.