Questionsexercises

11.1 For the binomial example in Section 11.3, calculate the probability of either one or zero errors.

11.2 For a roulette wheel with 18 red, 18 black, a zero, and a double zero, what is the probability of:

a. winning when you bet on black?

b. losing when you bet on red?

11.3 For a normal distribution with a mean value of 6 and a variance of 9, what is the probability that the random variable will exceed:

11.4 What is the probability of successful operation for 200 hours for a system with three subsystems with MTBFs of 100, 200, and 300 hours when the subsystems are:

a. in a ''series'' reliability configuration?

b. placed in a redundant configuration?

11.5 If the failure rate is 0.02 failure/hour and the mean-time-to-repair distribution is uniform in the range 2 to 10 hours, what is the system availability?

11.6 For threshold detection of a radar pulse in Gaussian additive noise, the pulse voltage is 14 volts, the threshold is set at 5 volts, and the noise power is 9 watts.

a. Find the detection and false-alarm probabilities.

b. Where would you put the threshold to obtain a false-alarm probability of approximately 0.02? What is the resultant detection probability?

11.7 The three one-sigma errors of a system, where the errors are additive and independent, are in the ratio 3:4:5, and the total allowable error variance is 0.5. What are the maximum values of the three independent errors?

11.8 What is the probability that a system will operate without failure:

(a) to its mean-time-between-failure (MTBF), and

(b) twice its mean-time-between failure? 