1 Question 2 To verify the identity of users who lose their password a website

1 question 2 to verify the identity of users who lose

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Question 2: To verify the identity of users who lose their password, a website asks 10 true-false security questions. Let Q equal the number of questions that are answered correctly. a) A naive hacker attempts to break in by randomly answering the 10 security questions. What is the probability distribution for the number of correctly answered questions Q ? b) Write a Python function that numerically evaluates the probabilities in part (a), and plot these probabilities as a function of Q . c) A more sophisticated hacker does research on the user whose account he seeks to break into, and gives the correct answer to each security question with probability 0.9. Give an equation for the distribution of the number of correctly answered questions Q , and write a Python function that numerically evaluates and plots these probabilities. Question 3: Let X be a continuous random variable representing the time, in hours, that it takes your laptop to backup its data to a server. Suppose that P ( X < 0) = 0 and P ( X > 4) = 0, because after 4 hours, the backup times out and fails. For 0 x 4, X has the probability density function f X ( x ) = cx 1 / 2 . a) What value of the constant c > 0 makes f X ( x ) a valid probability density function? b) What is the cumulative distribution function F X ( x ) ? What is the median of X ? c) What is the expected backup time E [ X ] ? d) What is the standard deviation of X ? 2
Question 4: Classifiers are of great use in diagnosing medical conditions based on symptoms. In this problem, you will consider a data set containing information about a set of patients (not a completely random sample of the population) who may or may not have heart disease.
• Fall '08
• Smyth,P
• Normal Distribution, Probability theory, probability density function, Yi, Cumulative distribution function

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