6. A thief can pick a lock quickly, but it takes time and practice to develop th

Question

6. A thief can pick a lock quickly, but it takes time and practice to develop this skill. We will model the amount of time a thief takes to pick a lock, in seconds, as a continuous random variable. Suppose the time that a novice takes to pick a lock follows a Normal distribution, with an average of = 25 seconds and a standard deviation of = 6 seconds; the time taken by an adept at lockpicking follows a Gamma distribution with -4 and 0.25; and the time taken by an expert locksmith follows an Exponential distribution with = 0.2. (a) Write the expected value of the time (in seconds) it will take a novice, an adept, and an expert to pick a lock, respectively. (b) [15 points] Suppose a thief picks a lock within 7 seconds. What is the probability this thief is an expert locksmith? Assume each skill level is equally likely initially.

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6. A thief can pick a lock quickly, but it takes time and practice to develop this skill. We will model the amount of time a thief takes to pick a lock, in seconds, as a continuous random variable. Suppose the time that a novice takes to pick a lock follows a Normal distribution, with an average of = 25 seconds and a standard deviation of = 6 seconds; the time taken by an adept at lockpicking follows a Gamma distribution with -4 and 0.25; and the time taken by an expert locksmith follows an Exponential distribution with = 0.2. (a) Write the expected value of the time (in seconds) it will take a novice, an adept, and an expert to pick a lock, respectively. (b) [15 points] Suppose a thief picks a lock within 7 seconds. What is the probability this thief is an expert locksmith? Assume each skill level is equally likely initially.

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