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1 If X has the CDF for x. 1).3 3.1. A computer virus is trying to corrupt two files. The first file will be corrupted with probability 0.4. Independently of it, the second file will be corrupted with probability 0.3. (a) Compute the probability mass function (pmf) of X', the number of corrupted files. (b) Draw a graph of its cumulative distribution function (cdf). 3.5. A software package consists of 12 programs, five of which must be upgraded. If 4 programs are randomly chosen for testing. (a) What is the probability that at least two of them must be upgraded? (b) What is the expected number of programs, out of the chosen four, that must be upgraded? 3.8. A computer user tries to recall her password. She knows it can be one of 4 possible passwords. She tries her passwords until she finds the right one. Let N' be the number of wrong passwords she uses before she finds the right one. Find E X) and Var(.")