If ∂f∂x=0∂𝑓∂𝑥=0, the function f(x,y)𝑓(𝑥,𝑦) has no dependence on the variable x𝑥.Select one:TrueFalse

If f(x)𝑓(𝑥) is a probability density function of a continuous random variable, then ∫∞−∞f(x)dx=∫−∞∞𝑓(𝑥)𝑑𝑥=  ?a.1b.undefinedc.Insufficient datad.0

Let f be a function such that 𝑓(−𝑥) = −𝑓(𝑥)  for all x. If ∫02𝑓(𝑥)𝑑𝑥=5, then ∫−22(𝑓(𝑥)+6)𝑑𝑥=Responses661616242434

Let 𝑓(𝑥)=𝑥3−3𝑥2+2𝑥f(x)=x 3 −3x 2 +2x. Find the maximum and minimum values of the function 𝑓(𝑥)f(x) on the interval [0,3][0,3].

Let X be a random variable with p.d.f 𝑓(𝑥) = {23 , 𝑤ℎ𝑒𝑛 𝑥 = 113 , 𝑤ℎ𝑒𝑛 𝑥 = 20, 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒Find themoment generating function , mean and standard deviation

Find the centroid of the region bounded by the curve 𝑦 = 𝑥 2 y=x 2 , the 𝑥 x-axis, and the lines 𝑥 = 0 x=0 and 𝑥 = 1 x=1.