ppr yun. 1pret the less. 5.22 Trajectory of an electric circuit. Researchers at

Question

ppr yun. 1pret the less. 5.22 Trajectory of an electric circuit. Researchers at the Uni versity of California-Berkeley have designed, built, and tested a switched-capacitor circuit for generating random signals (International Journal of Circuit Theory and Appli- cations, May-June 1990). The circuit's trajectory was shown to be uniformly distributed on the interval (0, 1). a. Give the mean and variance of the circuit's trajectory b. Compute the probability that the trajectory falls between .2 and .4 c. Would you expect to observe a trajectory that exceeds .995? Explain.

Explanation / Answer

a) mean =(0+1)/2 =0.5

variance =(b-a)/12 =(1-0)/12=1/12

b)P(0.2<X<0.4) =(0.4-0.2)/1 =0.2

c)probability of having trajectory to exceed 0.995 =P(X>0.995)=1-0.995=0.005

as above is having probability less then 0.05 level therefore it is an unusual event.

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