Answer to Question #313861 in Statistics and Probability for TIN

Question

The two most common type 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 X denote the number of syntax errors and Y the number of errors in logic made on the first run of a BASIC program. Assume that the joint density for (X,Y) is as shown in table 2:

x/y

0

1

2

3

0

.400

.100

.020

.005

1

.300

.040

.010

.004

2

.040

.010

.009

.003

3

.009

.008

.007

.003

4

.008

.007

.005

.002

5

.005

.002

.002

.001

a. Find the probability that a randomly selected program will have neither of these types of error.

b. Find the probability that a randomly selected program will contain at least one syntax error and at most one error of logic.

c. Find the marginal densities for X and Y

d. Find the probability that a randomly selected program contains at least two syntax errors.

e. Find the probability that a randomly selected program contains one or two errors in logic.

Answer 1

a. probability that randomly selected probability will have neither of these types of probability probability of X is equal to zero and y is equal to 0.4

b. P=0.1+0.02+0.005+0.04+0.01+0.004=0.179

c.

d. P=0.02+0.01+0.009+0.007+0.005+0.002+0.005+0.004+0.003+0.003+0.002+0.001=0.071

e. P=0.3+0.04+0.01+0.004+0.04+0.01+0.009+0.003=0.416