Chapter 10, Problem CCSQ

Suppose that X and Y have the following joint probability distribution 2 1 [0.1 y 4 0.151 P(X,Y) = x3 0.2 0.3 50.1 0.15 a) Evaluate the marginal distribution of X and Y. b) Find P(Y/X) and P(X/Y). c) Find P(Y=2/X=3). d) Find μx, μy, σ,σ and oxy.

Prelab Information Laboratory Preliminary Discussion Second-order RLC Circuit Analysis The second-order RLC circuit shown in figure 1 below represents all voltages and impedances as functions of the complex variable, s. Note, of course, that the impedances associated with R, RL, and Rs are constant independent of frequency, so the 's' notation is omitted. Again, one of the advantages of s-domain analysis is that we can apply all of the circuit analysis techniques learned for AC and DC circuits. ZI(s) Zc(s) Rs w RL ww + + VRS(S) VRL(S) VL(s) Vc(s) VR(S) R Vs(s) Figure 1: A second-order RLC circuit represented in the s-domain. To generate the s-domain expression for the output voltage, Vout(s) = VR(S), for the circuit shown in figure 1, we can apply voltage division in the s-domain as shown in equation 1 below. For equation 1 we define the following circuit parameters. RT=RS + RL + R where: R₁ = Total series resistance Rs Signal generator output resistance (fixed) Inductor internal…

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