Due Monday March 12 (60 points total) The two most common types of errors made b

Question

Due Monday March 12 (60 points total) The two most common types of errors made by programmers are syntax errors and errors in logic. For a simple language such as BASIC the number of such errors is usually small. Let Xdenote the number of syntax errors and Y the number of errors in logic made on the first run of a BASIC program. The sample space for X is (o. 1, 2, 3) and the sample space for Y is (0, 1.2.3, 4, 5). Assume that the joint density for (r D is shown in the following table: 1. 400 300 040 009 008 005 100 | 040 | .010 | .008 | .007 | .002 2 020 010 009 007 005 002 005 004 003 003 002 .001 a. (5 points) Find the probability that a randomly selected program will have neither of these types of errors b. (5 points) Find the probability that a randomly selected program will contain at least one syntax error and at most one error in logic. c. (5 points) Find the marginal densities for X and y d. (5 points) Find the probability that a randomly selected program contains at least two syntax errors. (5 points) Find the probability that a randomly selected program contains one or two e. errors in logic.

Explanation / Answer

Due Monday March 12 (60 points total) The two most common types of errors made by programmers are syntax errors and errors in logic. For a simple language such as BASIC the number of such errors is usually small. Let Xdenote the number of syntax errors and Y the number of errors in logic made on the first run of a BASIC program. The sample space for X is (o. 1, 2, 3) and the sample space for Y is (0, 1.2.3, 4, 5). Assume that the joint density for (r D is shown in the following table: 1. 400 300 040 009 008 005 100 | 040 | .010 | .008 | .007 | .002 2 020 010 009 007 005 002 005 004 003 003 002 .001 a. (5 points) Find the probability that a randomly selected program will have neither of these types of errors b. (5 points) Find the probability that a randomly selected program will contain at least one syntax error and at most one error in logic. c. (5 points) Find the marginal densities for X and y d. (5 points) Find the probability that a randomly selected program contains at least two syntax errors. (5 points) Find the probability that a randomly selected program contains one or two e. errors in logic.

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