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    I have no idea how to do this question and was wondering whether anyone was able to help me?

    The mode of a continuous random variable X is 1 and this is a stationary point. Given that X takes values over the range [0,3] find possible expressions for:
    a) the c.d.f of X
    b) the p.d.f of X

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    Think about what the question is asking. You have a crv taking values in [0,3], and you know that its pdf has a global maximum at 1. Using the additional requirement that the area under the graph of the pdf must equal 1, give an example of a possible pdf. There isn't a single right answer, you just need to find one such function - so go for something simple.
 
 
 
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