Below is a diagram of a portion of an electrical system where two wires (shown in...

  

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Below is a diagram of a portion of an electrical system where two wires (shown in blue) are electrically joined with two vias (shown in orange). As you can see the vias are connected in parallel (if the wires have no resistance). The combined resistance of the two vias is described as follows: Ruta:||PRvia2 = (Rytal R₁ + Rvia-T via - TOTAL - Or alternatively using conductance, G = 1/R, as follows: 1 vial Rvia2) -1 y 0.1 0.04 0.04 0.1 Gvia TOTAL X Rvia- When fabricated, the resistance (and thus conductance) of each via will be variable. Assume (unrealistically) that the conductance, of each via, can be modeled using uniformly distributed random variables X and Y with a maximum of 0.1 1/ohms and a minimum value of 0.04 1/ohms. The PDF is shown below. Further assume that the combined conductance, Gvia - TOTAL, is described by the random variable W=X+Y. – fxx(x,y) 1 via- TOTAL = fxx(x,y) = 0.06 (Gvia1 + Gvia2) 2 ) 0, .04y <.1, .04 < x <.1 otherwise a) Determine an expression for the CDF for W. (Do not evaluate integrals, just set them up.) b) Assume that the system will not meet spec if the combined resistance is greater than 10 ohms. Determine the probability that the system does not meet spec. Below is a diagram of a portion of an electrical system where two wires (shown in blue) are electrically joined with two vias (shown in orange). As you can see the vias are connected in parallel (if the wires have no resistance). The combined resistance of the two vias is described as follows: Ruta:||PRvia2 = (Rytal R₁ + Rvia-T via - TOTAL - Or alternatively using conductance, G = 1/R, as follows: 1 vial Rvia2) -1 y 0.1 0.04 0.04 0.1 Gvia TOTAL X Rvia- When fabricated, the resistance (and thus conductance) of each via will be variable. Assume (unrealistically) that the conductance, of each via, can be modeled using uniformly distributed random variables X and Y with a maximum of 0.1 1/ohms and a minimum value of 0.04 1/ohms. The PDF is shown below. Further assume that the combined conductance, Gvia - TOTAL, is described by the random variable W=X+Y. – fxx(x,y) 1 via- TOTAL = fxx(x,y) = 0.06 (Gvia1 + Gvia2) 2 ) 0, .04y <.1, .04 < x <.1 otherwise a) Determine an expression for the CDF for W. (Do not evaluate integrals, just set them up.) b) Assume that the system will not meet spec if the combined resistance is greater than 10 ohms. Determine the probability that the system does not meet spec.

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a Determine an expression for the CDF for W The CDF for W denoted as FWw represents the probability ... View the full answer