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1. The lifetime T (in days) of an electrical component has reliability function given by: R(t) = e-0.01t for time t > 0. An electrical system consists of four such components. The system continues to function if at least one component is still 'alive' and the system is repaired (by replacing all the components) when all components have expired.
(a) Find the probability density function (PDF) of T, the lifetime of a component in the system.
(b) Show that this is a valid PDF.
(c) Find the reliability function for the system.
(d) Find the probability that the system lasts for longer than 1 year (365 days).
(e) Simulate the lifetime of the system.
(f) Set the random number seed using set.seed(1). Then simulate 20 lifetimes for the system. Calculate the sample mean lifetime of the system using your 20 simulated values.
ABC is a triangle right angled at c. let BC=a, CA=b, AB=c and lrt p be the length of the perpendicular from C on AB. prove that cp=ab and 1/p2=1/a2+1/b2
solve for x and y 2x+3y=12 and 30x+11y=112
Ask question #Min 4.4238/[1.047+{1.111*[9.261/7.777]}*1.01
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Find no. of non negative integral solutions x 1 +x 2 +x 3 +4x 4 =20 Solution) 140. Break them into prime factors . Put 4 = 2^2 and every variable will have factors in 2,3,5 with
Ahmad borrowed $450000.00 at 3% compounded semi-annually for ten years to buy an apartment. Equal payments are made at the end of every six months. a) Determine the size of the se
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