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If I have a pdf represented by the following function:

$$f(x) = \dfrac{3(x+x^2)}{14} $$ from $0<x<2$. I know I must look for the maximum value $f(x)$ achieves and the mode will be the $x$ value associated with it. Is this a case where there is no mode, which is my suspicion?

user3753
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    The function is increasing on the interval $[0,2]$ so its maximum value is at $x=2$. Do you know the definition of mode for a continuous pdf? If not, try Google. – John Wayland Bales Jun 08 '19 at 16:37
  • Since 2 is not included though would this mean there is no mode? I understand that it is increasing the entire interval. – user3753 Jun 08 '19 at 16:57
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    By pdf do you mean probability density function or probability distribution function? I ask because the second meaning is ambiguous, since it can mean cumulative distribution function. Since you are using lower case $f$ I assume you mean probability density function. For a continuous variable $X$, the probability that $X$ actually equals the mode is always $0$, so I see no reason that the mode in this case would not be $2$. – John Wayland Bales Jun 08 '19 at 17:26

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