Variance of the time, the expected value and the variance

Variance of the time

Assignment Help Basic Statistics

Reference no: EM131005669

There are two machines, one of which is used as a spare. A working machine will function for an exponential time with rate λ and will then fail. Upon failure, it is immediately replaced by the other machine if that one is in working order, and it goes to the repair facility. The repair facility consists of a single person who takes an exponential time with rate μ to repair a failed machine. At the repair facility, the newly failed machine enters service if the repairperson is free. If the repairperson is busy, it waits until the other machine is ?xed; at that time, the newly repaired machine is put in service and repair begins on the other one. Starting with both machines in working condition, ?nd

(a) the expected value and

(b) the variance of the time until both are in the repair facility.

Reference no: EM131005669

Questions Cloud

Average number of taxis waiting : (a) the average number of taxis waiting, and (b) the proportion of arriving customers that get taxis.

What is the new pressure in the tank : A sealed rigid tank is filled with 1 kg of steam at 200 °C and 10 bar. What is the volume of the tank? 0.5 kg of steam are removed from the tank. If the temperature remains at 200 °C, what is the new pressure in the tank?

Determine the coordinates of the maximum point : Determine the coordinates (tm, ym) of the maximum point of the solution as function of β. Determine the smallest value of β for which ym ≥4. Determine the behaviour of tm and ym as β→∞

Distribution of the number of customers : Customers arrive at a single-server queue in accordance with a Poisson process having rate λ. However, an arrival that ?nds n customers already in the system will only join the system with probability 1/(n + 1). That is, with probability n/(n + 1)..

Variance of the time : the expected value and the variance of the time until both are in the repair facility. In the long run, what proportion of time is there a working machine?

How much heat is removed during the cooling step : A sealed tank contains saturated steam at 5 bar. The volume of the tank is1m3. Heat is added until the pressure in the tank pressure doubles. What is the final temperature?

Calculate the amount of heat associated with this process : Calculate the amount of work necessary for the reversible compression of 1 kg of steam from 3 bar to 7 bar. The compression is to take place in a cylinder fitted with a weightless piston at the constant temperature of 250 °C. Calculate the amount ..

What is your recommendation for the required air flow rate : What is your recommendation for the required air flow rate (in SCFM) to produce water that meets EPA standards.

Determine the energy balance for this process : An insulated cylinder fitted with a weightless latched piston contains steam at 5 bar, 300 °C. The piston is unlatched and the steam expands against ambient air at P = 1 bar. The temperature of steam in the final state is 142 °C. Determine the ene..

User Account

All Pages