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Difficulty starting degree level questions watch

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    Hi,
    I've recently been given these questions on a worksheet, but I've been stumped at this one. Anyone got any pointers as to how I should go about starting it? Thanks muchly in advance
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    (Original post by thomoski2)
    Hi,
    I've recently been given these questions on a worksheet, but I've been stumped at this one. Anyone got any pointers as to how I should go about starting it? Thanks muchly in advance
    You should know that adding up all the possible probabilities must output the total probability of 1.

    This means that for a probability distribution f_X(x) you must have \displaystyle \int_{\mathbb{R}} f_X(x) .dx = 1.

    Applying this to your question, since f is a piecewise function, you need to split the integral into 3 different ones over the regions (-\infty, 0], [0,5], and [5, \infty). However, note that f(x)=0 for the first and third interval therefore those integrals will just be 0 and hence you simply need say that \displaystyle \int_0^5 f(x) .dx = 1
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    (Original post by RDKGames)
    You should know that adding up all the possible probabilities must output the total probability of 1.

    This means that for a probability distribution f_X(x) you must have \displaystyle \int_{\mathbb{R}} f_X(x) .dx = 1.

    Applying this to your question, since f is a piecewise function, you need to split the integral into 3 different ones over the regions (-\infty, 0], [0,5], and [5, \infty). However, note that f(x)=0 for the first and third interval therefore those integrals will just be 0 and hence you simply need say that \displaystyle \int_0^5 f(x) .dx = 1
    What about (b) and (c), I’m kinda hitting a blank with those two
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    (Original post by thomoski2)
    What about (b) and (c), I’m kinda hitting a blank with those two
    \displaystyle \mathbb{E}(T) =\int_0^5 tf(t) \, \mathrm{d}t
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    (Original post by RDKGames)
    You should know that adding up all the possible probabilities must output the total probability of 1.

    This means that for a probability distribution f_X(x) you must have \displaystyle \int_{\mathbb{R}} f_X(x) .dx = 1.

    Applying this to your question, since f is a piecewise function, you need to split the integral into 3 different ones over the regions (-\infty, 0], [0,5], and [5, \infty). However, note that f(x)=0 for the first and third interval therefore those integrals will just be 0 and hence you simply need say that \displaystyle \int_0^5 f(x) .dx = 1
    You also need the function to be non-negative.
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    (Original post by Zacken)
    \displaystyle \mathbb{E}(T) =\int_0^5 tf(t) \, \mathrm{d}t
    Awesome, that’s a huge help with c, what about b?
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    (Original post by thomoski2)
    Awesome, that’s a huge help with c, what about b?
    The quickest 10% of the students will be those who complete the test within a certain amount of time \tau after it starts, which you got to show is \tau \approx 1.4357, such that P(T \leq \tau) = 0.1
 
 
 
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