P(0<x<4)=P(x=1)+P(x=2)+P(x=3) =k+2k+2k=5k As we know that, sum of all probability events =1 ⇒0+k+2k+2k+3k+k2+2k2+7k2+k=1 ⇒10k2+9k−1=0 ⇒(10k−1)(k+1)=0 ⇒k=
1
10
,[k=−1 (rejected) because probability of any event lies between 0 to 1 ] ∴P(0<x<4)=5×