$1.$ The state space of a Markov chain is the nonnegative integers. When in state i$>0$ it moves next to state i$+1$ with probability $1/4$ and to state i$1$ with probability $3/4.$ When in state $0$ it stays there with probability $3/4$ and otherwise transitions to state $1.$ Denote by pi the stationary distribution of the chain. If pi$0=2/3,$ then what is pi$1?($Answer a decimal number with two significant digits; for example $0\mathrm{.}37).$

$2.$ The chain described in the previous problem is time reversible.

a$.$ true

b$.$ false