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In a support system in the U.S. space program, a single crucial component works only 85% of the time. In order to enhance the reliability of the system, it is decided that 3 components will be installed in parallel such that the system fails only if they all fail. Assume the components act independently and that they are equivalent in the sense that all 3 of them have an 85% success rate. Consider the random variable X as the number of components out of 3 that fail.
(a) Write out a probability function for the random variable X.
(b) What is E(X) (i.e., the mean number of components out of 3 that fail)?
(c) What is Var(X)?
(d) What is the probability that the entire system is successful?
(e) What is the probability that the system fails?
(f) If the desire is to have the system be successful with probability 0.99, are three components sufficient? If not, how many are required?
Calculate the acceleration in meters per secondsquared and compare to the value of the gravitational accelerationnear the Earth's surface (9.8 m/s^2)
By continuous discharge measurements the discharge in stream was determine over a 3-year period. After the data were assembled, it was found that the discharge exceeded 120 cfs 3 percent of the time;
Three particles are sliding along a flat, frictionless surface. mA = 0.4 kg, mB = 0.5 kg, and mC = 0.4 kg. Before any collisions take place, vA = 15i m/s, vB = 10im/s, and vC = 5 m/s. e = 0.85 between A and B and e = 0.6 between B and C.
The sodium cyanide solution ([NaCN]-total = 0.01 M) is kept at pH 10.4. The pH is kept high to keep the cyanide in the CN- form. If CN protonates by the reverse of the HCN dissociation reaction,
A random variable X has density function f(x) = CX^2 1
An aggregate blend is composed of 53% coarse aggregate by weight (sp. gr. 2.702), 43% fine aggregate (sp. gr. 2.621), and 4% filler (sp. gr. 2.779)/ The compacted specimen contains 6% asphalt binder (sp. gr. 1.052) by weight of total mix, and has a b..
You have been asked to design a hoisting system and a demolition catch system for the superstructure of a bridge that you are removing. Discuss in detail the steps you would take in order to be able to provide the necessary information
A paper plant is proposed for a location 1 km upwind from a town. It will emit 40 g/s of hydrogen sulfide, which has an odor threshold of about 0.1 mg/m 3. Winds at the effective stack are typically 4 m/s owing toward the town.
The frame is supported in part by normal and friction forces between the wall and the plate at A. Determine the friction force exerted on the plate at A. Also determine the minimum required coefficient of friction at A for the frame to remain in e..
An entrepreneurial new civil engineering graduate started a lab for testing endocrine disrupting compounds. The lab just broke even the first year, but in years 2 through 5, it made a profit of $97,000 each year.
An HSS 10×8×3?16 is used as a compression member with one end pinned and the other end fixed against rotation but free to translate. The length is 12 feet. Compute the nominal compressive strength for A500 Grade B steel
A water sample has phenolphthalein alkalinity (PPA) of 30 mg/L as CaCO3 and total alkalinity (TA) of 84 mg/L as CaCO3. If OH alkalinity is 5.3 mg/L as CaCO3, Calculate the alkalinity due to HCO3- and CO3-2.
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