Question

Find the value of 'k' if the density function is f(x) = kx ,0 <x< 3.​

Answer 1

Answer:

∵ the value of a probability density function over the whole range is equal to ′1′

i) ∴∫02f(x)dx=∫02kxdx=1

                   ⇒K[2x2]02=1

                   ⇒k[24−0]=1

                   ⇒k×2=1

                   ⇒k=21

ii) P(1<x<2)

                  ∫12f(x)dx=∫1221xdx Putting value of k=21

                 =21[2x2]12

                 =21[24−21]