S1 Past paper help?!

I have attached the problem and my working, can anyone see where ive got wrong? why is what ive done different to doing F(3) = 1?

Thanks!

You're confusing it for the probability density function, when you would add f(1), f(2) and f(3).

Remember that for the cumulative distribution you're 'adding up' - so in your calculations you've triple-counted P(X<1) and double-counted 2 P(X<2). Can you see why? Then you'll see that your calculation sums to more than 1.

Hey, cant see how come ive triple-counted P(X<1) and double-counted 2 P(X<2) care to explain? thanks for your time!

Well, you already know from the solution that F(3) = 1 - that is, P(X less than/equal to 3) = 1.

Which is made up of P(X less than / equal to 1) and P(X greater than 1 and less than or equal to 3). A similar thing for P(X<1) being part of P(X<2) and P(X<2) being part of P(X<3).

But that was just a side note - you've used that the sum of the probabilities of each event add up to 1, but that's not what the cumulative distribution finds so you can't put in F(1), F(2) and F(3) and add them together.