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c.d.f p.d.f S2 Maths questions

I have to determine whether the following questionis a c.d.f or not:

F(x)= 0, x<0
3x-2x^2, 0_<x_<1
1, x>1
The issue is I thought to determine if you have a c.d.f in this case F(1) should equal 1 but the mark scheme says F'(x)<0 so it isn't a c.d.f. Why do you need to differentiate?
A c.d.f should look like an S shape that reaches its maximum of 1 at x=1 (usually plateauing). This question attempts to trick you by giving you a quadratic function where F(1) = 1. However, in the range of 0<x<1 (greater or equal signs), this is not the maximum (which can be found at F'(x) = 0). In fact, it's going down (hence the derivative F'(1) = -1)

Plotting the the function in a graph helps to visualize - the function looks a bit like this:
not a cumulative.png

Hope this helps :smile:
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Avatar for Abby5001
Abby5001
OP
9
Original post by PeterTheHe
A c.d.f should look like an S shape that reaches its maximum of 1 at x=1 (usually plateauing). This question attempts to trick you by giving you a quadratic function where F(1) = 1. However, in the range of 0<x<1 (greater or equal signs), this is not the maximum (which can be found at F'(x) = 0). In fact, it's going down (hence the derivative F'(1) = -1)

Plotting the the function in a graph helps to visualize - the function looks a bit like this:
not a cumulative.png

Hope this helps :smile:


so are you basically saying because when x=1 on the graph, the graph is not at its peak therefore F(1) is not the maximum But by using dy/dx I can find the maximum point? I would never know I needed to do this so is there any way aside from drawing the graph I could get this conclusion? Thanks


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Well it doesn't hurt to check function (through differentiation or -b/2a). They put questions like this in to "separate the men from the boys" and its honestly just a matter of thoroughness. F'(1) = -1 which means the (local) maximum has already been reached.
Reply 4
Avatar for Abby5001
Abby5001
OP
9
Original post by PeterTheHe
Well it doesn't hurt to check function (through differentiation or -b/2a). They put questions like this in to "separate the men from the boys" and its honestly just a matter of thoroughness. F'(1) = -1 which means the (local) maximum has already been reached.


Alright I will do that in future thankyou


Posted from TSR Mobile

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