Total probability and bayes formulae

Reference no: EM13246913

A Crosslinked System. Each of the five components in a crosslinked system (shown) is operational in a time interval ?T with the probability of 0.8. The components are independent.

(a) Find the probability that the system is operational during the time period ?T .

(b) If the system was operational during ?T , what is the probability that component E3 had been operational?

1189_Total probability and Bayes formulae.png

Figure 1: A crosslinked system. If E3 is operational both branches exiting from it are active (think about electricity ?ow). If E3 is not operational neither of the two branches exiting from it is active.

Hint: The problem combines circuits and Bayes' formula. Discuss how the circuit simplifies when component E3 works and, alternatively, when it fails. When E3 works, is E1 relevant? What are the hypotheses needed for the total probability and Bayes' formulae?

Reference no: EM13246913

Questions Cloud

What is the magnetic moment of the loop : The plane of a 5.10cm by 9.00cm rectangular loop of wire is parallel to a 0.220T magnetic field, What is the magnetic moment of the loop

Find expression for torsional constant k in terms of moment : A thin metal disk of mass m=2.00 x 10^-3 kg and radius R=2.20cm is attached at its center to a long fiber. When the disk is turned from the relaxed state through a small angle theta, the torque exerted by the fiber on the disk is proportional to t..

Describe electrophilic aromatic substitution : In electrophilic aromatic substitution, why does an amide group direct substitution to a position opposite to it on the aromatic ring. The N donates electron density to the ring by induction and destabilizes the intermediate that forms meta to it

Determine the angular speed : An old-fashioned vinyl record rotates on a turntable at 49rpm . What are the angular speed in rad/s and the period of the motion

Total probability and bayes formulae : Find the probability that the system is operational during the time period and what is the probability that component E3 had been operational?

Define what is the concentration ratio of co2 : What is the concentration ratio of CO2 (usually written as H2CO3) to HCO3- in blood at pH = 7.40. (carbonic acid Ka1 = 4.3 x 10-7)

What is the theoretical barrier height of semiconductor : Consider two Si samples; one is p-type doped to 1018/cm3 acceptor atoms and the other one n-type doped to 1015/cm3 donor atoms at room temperature (300K). a. Draw the band diagram associated with p-type and n-type semiconductors, noting the various..

Compute the mass of sodium acetate : Calculate the mass of sodium acetate that must be added to 500.0 mL of 0.200 M acetic acid to form a pH = 5.00 buffer solution.

Calculate the energies of three lowest states of positronium : A positron is an antimatter particle identical in mass to an electron but with a positive charge, Calculate the energies of the three lowest states of positronium

User Account

All Pages