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Size:  54.3 KBCan someone please explain to me why the solution to question 3a as shown in the solution photo is true and why?
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    (Original post by BenRichi_)
    Name:  image.jpeg
Views: 66
Size:  54.3 KBCan someone please explain to me why the solution to question 3a as shown in the solution photo is true and why?
    Do you understand what a cumulative distribution function is? The C.D.F F(x) tells you the probability \mathbb{P}(X \leq x) i.e: it is the 'area' under your graph.

    Since F(2) = 1, this represents your total area which is k(2^2 -2) = 1 and you know the total area under your graph has to be 1 since probabilities can never exceed 1. Hence the equation follows and you solve it to fine k.

    Edit: If you're having trouble understanding what a CDF is/does, this video may prove useful.
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    (Original post by Zacken)
    Do you understand what a cumulative distribution function is? The C.D.F F(x) tells you the probability \mathbb{P}(X \leq x) i.e: it is the 'area' under your graph.

    Since F(2) = 1, this represents your total area which is k(2^2 -2) = 1 and you know the total area under your graph has to be 1 since probabilities can never exceed 1. Hence the equation follows and you solve it to fine k.

    Edit: If you're having trouble understanding what a CDF is/does, this video may prove useful.
    Thank you for your response, I do understand what a c.d.f is and I understand that the area underneath it is 1 however I don't understand why F(2) = 1
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    (Original post by BenRichi_)
    Thank you for your response, I do understand what a c.d.f is and I understand that the area underneath it is 1 however I don't understand why F(2) = 1
    The piecewise function says that F(y) = 1 for y > 2 and from this you can infer that F(2)  = 1, it's mainly 'cause the question is crappily written to be fair, they should have said y \geq 2; so I understand your confusion.
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    (Original post by Zacken)
    The piecewise function says that F(y) = 1 for y > 2 and from this you can infer that F(2)  = 1, it's mainly 'cause the question is crappily written to be fair, they should have said y \geq 2; so I understand your confusion.
    Ah okay, thank you for the help it is much appreciated!
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    (Original post by BenRichi_)
    Ah okay, thank you for the help it is much appreciated!
    No worries.
 
 
 
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