Suppose a system consists of 12 components connected in series, which must all operational for the...

Suppose a system consists of 12 components connected in series, which must all operational for the system to work. If there 5 components of one type with a mean lifetime of 3 years. 7 of the components of a different type and have a mean lifetime of 2 years. Assume the lifetimes are exponentially distributed. Let X be the first time the system stops working.

(a) Find the probability that X is less than 1 and describe in words what this event means.

(b) Find the CDF for X.

(c) Find the CDF for X if the number of type-1 components is n and the number of type-2 components is k.

Expert Solution

orchestra answered 2 years ago

Two continuous stirred-tank fermenters are connected in series, the first having an operational volume of 100...

Two continuous stirred-tank fermenters are connected in series, the first having an operational volume of 100 L and that of the second being 50 L. The feed to the first fermenter is sterile and contains 5000 mg/L of substrate, being delivered to the fermenter at 18 L/h. If the microbial growth can be described by the Monod kinetic model with µm= 0.25 h-1 and Ks = 120 mg/l. What would happen if the flow were from the 50 L fermenter...

which circuits must not be connected to any system containing trolley wires with a ground return?...

which circuits must not be connected to any system containing trolley wires with a ground return? a. ground wires b. grounding conductors c.circuits for lighting and power d. ungrounded trolley wires

The Electron Transport System consists of a series of enzyme complexes that are embedded in the...

The Electron Transport System consists of a series of enzyme complexes that are embedded in the inner mitochondrial membrane. Which one of the following statements is NOT TRUE of mitochondria or the electron transport chain? a. Tissues that run aerobic metabolism are enriched in mitochondria. b. Glycolysis, the first stage of carbohydrate breakdown, occurs in the inner mitochondrial membrane. c. Coenzyme Q10 is a critical electron carrier imbedded in the inner mitochondrial membrane. d. The Electron Transport System is the...

(Only need d, e, and f) A resistor R = 12 MΩis connected in series with...

(Only need d, e, and f) A resistor R = 12 MΩis connected in series with a capacitor C = .7 μF and a battery V = 12 volts. a) What is the time constant of this circuit? b) How many seconds will it take for the voltage across the capacitor to equal 10 volts? c) How many seconds will it take for the current to drop to 20% of its maximum value? d) After 30 seconds, what are the...

A system consists of two components. The probability that the second component functions in a satisfactory...

A system consists of two components. The probability that the second component functions in a satisfactory manner during its design life is 0.9, the probability that at least one of the two components does so is 0.94, and the probability that both components do so is 0.85. Given that the first component functions in a satisfactory manner throughout its design life, what is the probability that the second one does also? (Round your answer to three decimal places.)

1.) A mass-spring system consists of an object of mass 1 Kilogram connected to a spring...

1.) A mass-spring system consists of an object of mass 1 Kilogram connected to a spring with a stiffness of 9. The damping constant is 6. Derive the function (1) that determines the distance from the equilibrium point if the initial position is 3 meters from the equilibrium point and the initial speed is 3 meters per second. a.) What is the maximum distance from the equilibrium point? b.) Determine the general solution of the nonhomogeneous linear differential equation using...

An inductor is connected in series to a fully charged capacitor. Which of the following statements...

An inductor is connected in series to a fully charged capacitor. Which of the following statements are true? Check all that apply. - As the capacitor is charging, the current is increasing. - The stored electric field energy can be greater than the stored magnetic field energy. - As the capacitor is discharging, the current is increasing. - The stored electric field energy can be less than the stored magnetic field energy. - The stored electric field energy can be...

A system consisting of two components is subject to a series of shocks that arrive according...

A system consisting of two components is subject to a series of shocks that arrive according to a Poisson process with a rate of one per day. Half the shocks cause no damage, one in ten damages component 1 alone, one in five damages component 2 alone, and the rest damage both components. Note that if only one component is functioning, and a shock occurs that would damage both components, the functioning component is damaged. Compute the probability that the...

Engineering system of type k-out-of-n is operational if at least k out of n components are...

Engineering system of type k-out-of-n is operational if at least k out of n components are operational. Otherwise, the system fails. Suppose that a k-out-of-n system consists of n identical and independent elements for which the lifetime has Weibull distribution with parameters r and λ. More precisely, if T is a lifetime of a component, P(T ≥ t) = e−λtr, t ≥ 0. Time t is in units of months, and consequently, rate parameter λ is in units (month)−1. Parameter...

An electrical system consists of 2 components (C1 and C2) functioning independently and are set in...

An electrical system consists of 2 components (C1 and C2) functioning independently and are set in a parallel layout. The failure time of each component follows an exponential distribution with rate 2 every year. Identify the failure density of system if i) the system functions if and only if both components function. Hence, calculate the probability of the system failing in less than 8 months. ii) the system can function only on anyone functioning component. Hence, determine the probability of...

Question