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Thread: Finding cumulative distribution function F(x)

  1. #1
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    Finding cumulative distribution function F(x)

    At the bottom, when he's defining F(x), why is it 1 when x is greater than or equal to 2? Shouldn't it be zero?
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  2. #2
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    Re: Finding cumulative distribution function F(x)

    Quote Originally Posted by asilvester635 View Post
    At the bottom, when he's defining F(x), why is it 1 when x is greater than or equal to 2? Shouldn't it be zero?
    Because the total probability is $1$, once we 'pass' $2$ the total probability has accumulated and remains constant for $x\ge2$
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    Re: Finding cumulative distribution function F(x)

    Because the probability is non-negative, the cumulative probability distribution function is always an increasing function.
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    Re: Finding cumulative distribution function F(x)

    Quote Originally Posted by asilvester635 View Post
    At the bottom, when he's defining F(x), why is it 1 when x is greater than or equal to 2? Shouldn't it be zero?
    Actually a CDF, $\mathcal{F}$, is non-decreasing function: $(-\infty,\infty)\to[0,1]$. In addition, the function $\mathcal{F}$ is right-hand continuous.
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    Re: Finding cumulative distribution function F(x)

    Thanks!!!!
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