A pdf (f(x)) can never take a negative value as it is not possible to have a negative probability. The curve which goes below the x-axis is therefore not a pdf.



A pdf cannot have a 1 to many relationship, one outcome (x value) cannot map to two different probabilites, hence the red curve cannot represent a probability density function.



All remaning curves could represent a pdf.



The maximum value of the random variable of a circular arc pdf passing through the origin will be equal to the diamater.We will achieve the largest x value when we have a semi-circle passing through the origin. The maximum value is therefore twice the radius = 2.