Compute the steady-state probabilities and the expected number of HAPPY-Q micro-organisms in this vial in steady-state. Please solve both parts.
a) The steady-state probabilities can be calculated using the formula: pi_j = lambda_j / sum(lambda_i) and the expected number of HAPPY-Q micro-organisms in steady-state can be calculated using the formula: E[N] = sum(j x pi_j)
b) The steady-state probabilities can be calculated using the formula: pi_j = mu_j / sum(mu_i) and the expected number of HAPPY-Q micro-organisms in steady-state can be calculated using the formula: E[N] = sum(j x pi_j)
c) The steady-state probabilities can be calculated using the formula: pi_j = lambda_j / mu_j and the expected number of HAPPY-Q micro-organisms in steady-state can be calculated using the formula: E[N] = sum(j x pi_j)
d) The steady-state probabilities can be calculated using the formula: pi_j = mu_j / lambda_j and the expected number of HAPPY-Q micro-organisms in steady-state can be calculated using the formula: E[N] = sum(j x pi_j)