Consider the birth$-$and$-$death process with the following mean rates. The birth rates are: lambda $0=2,{}_1=3,2=2,l_{\text{a}\text{m}\text{b}\text{d}\text{a}}^3=1,a_n$ lambda $a_n=0,$ for $n>3.$ The death rates are ${}_1=3,{}_2=4,{}_3=1,$ and ${}_n=2$ for $n>4.$

Develop the balance equations using the space below to show your solutions.

Solve these equations to find the steady$-$state probability distribution $P_0,P_1,P_2,P_3,P_4.$