# Thread: Finding cumulative distribution function F(x)

1. ## 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?

2. ## Re: Finding cumulative distribution function F(x)

Originally Posted by asilvester635
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 $x\ge2$

3. ## Re: Finding cumulative distribution function F(x)

Because the probability is non-negative, the cumulative probability distribution function is always an increasing function.

4. ## Re: Finding cumulative distribution function F(x)

Originally Posted by asilvester635
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.

Thanks!!!!