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A-Level Statistics 2 Continuous Random Variables Help

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1. Can someone please explain to me why the solution to question 3a as shown in the solution photo is true and why?
2. (Original post by BenRichi_)
Can 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 tells you the probability i.e: it is the 'area' under your graph.

Since , this represents your total area which is 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 .

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

Since , this represents your total area which is 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 .

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
4. (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
The piecewise function says that for and from this you can infer that , it's mainly 'cause the question is crappily written to be fair, they should have said ; so I understand your confusion.
5. (Original post by Zacken)
The piecewise function says that for and from this you can infer that , it's mainly 'cause the question is crappily written to be fair, they should have said ; so I understand your confusion.
Ah okay, thank you for the help it is much appreciated!
6. (Original post by BenRichi_)
Ah okay, thank you for the help it is much appreciated!
No worries.

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