Sojourn time in a state for a Markov chain. Prove E[τ _(i)]=(1)/(1-p_(ii))
where τ _(i) , is the expected sojourn time (in units of the sampling interval) of a Markov chain in state i (mode).

a. E[τ _(i)]=(1)/(1-p_(ii))
b. E[τ _(i)]=(1)/(p_(ii))
c. E[τ _(i)]=(p_(ii))/(1)
d. E[τ _(i)]=(p_(ii))/(p_(ii)-1)