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Applied Statistics and Probability for Engineers | 6th Edition | ISBN: 9781118539712 | Authors: Douglas C. Montgomery, George C. Runger
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An article in Genome Research [“An Assessment of Gene

Chapter 2, Problem 223SE

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QUESTION:

An article in Genome Research [“An Assessment of Gene Prediction Accuracy in Large DNA Sequences” (2000, Vol. 10, pp. 1631–1642)], considered the accuracy of commercial software to predict nucleotides in gene sequences. The following table shows the number of sequences for which the programs produced predictions and the number of nucleotides correctly predicted (computed globally from the total number of prediction successes and failures on all sequences).

Assume the prediction successes and failures are independent among the programs.

(a) What is the probability that all programs predict a nucleotide correctly?

(b) What is the probability that all programs predict a nucleotide incorrectly?

(c) What is the probability that at least one Blastx program predicts a nucleotide correctly?

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QUESTION:

An article in Genome Research [“An Assessment of Gene Prediction Accuracy in Large DNA Sequences” (2000, Vol. 10, pp. 1631–1642)], considered the accuracy of commercial software to predict nucleotides in gene sequences. The following table shows the number of sequences for which the programs produced predictions and the number of nucleotides correctly predicted (computed globally from the total number of prediction successes and failures on all sequences).

Assume the prediction successes and failures are independent among the programs.

(a) What is the probability that all programs predict a nucleotide correctly?

(b) What is the probability that all programs predict a nucleotide incorrectly?

(c) What is the probability that at least one Blastx program predicts a nucleotide correctly?

ANSWER:

Solution:

Step 1 of 4:

The experiment under consideration is study of accuracy of commercial software in predicting nucleotides in gene sequence.

The data regarding number of sequences for which program produced prediction and the proportion of correct predictions.

Number of sequences

Proportion

GenScan

177

0.93

Blastx Default

175

0.91

Blastx topcomboN

174

0.97

Blastx 2 stages

175

0.90

Gene wise

177

0.98

Procrustes

177

0.93

Using this data we need to find the required values.

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