Edexcel S2 Book Mixed Exercise 4C help!

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Catful1
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Hi there - I hope someone can help! I am working through the book above and am on exercise 4c, but I don't understand how two of the answers have been worked out.

1f) I don't understand why the answer is 0 for X=4. I have worked out the c.d.f as 1/7x+1/7 so don't understand why the book says 0
4c) I have worked out the c.d.f to 1/20c-1/20 so don't understand why the answer for probability at least 8 uses 12-8 instead of 20-8.

Any help much appreciated.

Thanks
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Indeterminate
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(Original post by Catful1)
Hi there - I hope someone can help! I am working through the book above and am on exercise 4c, but I don't understand how two of the answers have been worked out.

1f) I don't understand why the answer is 0 for X=4. I have worked out the c.d.f as 1/7x+1/7 so don't understand why the book says 0
4c) I have worked out the c.d.f to 1/20c-1/20 so don't understand why the answer for probability at least 8 uses 12-8 instead of 20-8.

Any help much appreciated.

Thanks
It would help if you could post the Q as a lot of people on this forum won't have access to the book (including me, a uni student).
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Catful1
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Thanks - the questions are below:
1f) the continuous random variable X is uniformly distributed over the interval (-2,5). Find P(X=4)
4c) a child has a pair of scissors and a piece of string 20cm long, which has a mark on one end. the child cuts the string, at a randomly chosen point, into two pieces. Let X represent the length of the piece of string with the mark on it. Using your model, calculate the probability that the shorter piece of string is at least 8cm long.

thanks
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kelechi96
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I'm sorry I'm raising the dead here, but I have problems with this too and I'm unsure as to whether to create a new thread or just raise this one.

My problem was with Ex 4C Qu 4C which has been stated by the previous poster... any help?

As for 1f) The answer is 0, because for any continuous random variable P(X=a) = 0 where a is some constant. The reasons for this is how you find the probability of any continuous random variable i.e by integrating it's probability density function... that is to say by finding the area under the curve within the limits. So for the p.d.f:

p.d.f = f(x)

\displaystyle\int^b_a f(x)\ dx = P(a<X<b) = P(a \leq X \leq b)
(Because the difference between \leq and < is infinitesimal... so for all intents and purposes the difference is zero.)

When we evaluate the integral of f(x) with upper limit b and lower limit a we generate a function, let's call it int(x) which is the indefinite integral of f(x) evaluated at point x such that we can write \displaystyle\int^b_a f(x)\ dx = int(b) - int(a)

Now here's why P(X=a) = 0, because when we evaluate the integral of f(x) with upper limit a and lower limit a we get \displaystyle\int^a_a f(x)\ dx = int(a) - int(a) = 0

A rather long explanation for a relatively simple question.
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FarahMJ
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Hello could you please answer 4C? I also don't know why they used 12-8 and not 20-8.
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Lot7
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(Original post by FarahMJ)
Hello could you please answer 4C? I also don't know why they used 12-8 and not 20-8.
If you go onto the Maths and Physics tutor website, there is a solution bank with all worked answers to the textbook
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