Intermediate Probability Theory for Biomedical Engineers - JohnD. Enderle

BIVARIATE RANDOM VARIABLES 103

n), (f ) pz,w, (g) pz, (h) pw, (i) pz,w|z>2w, (j) E(z), (k) E(w), (l) E(z| z > 2w), (m) σz2,

(n) σz2|z>2w, (o) σz,w, (p) σz,w|z>2w, (q) ρz,w, (r) ρz,w|z>2w.

92. Professor Rensselaer has been known to make an occasional blunder during a lecture. The probability that any one student recognizes the blunder and brings it to the attention of the class is 0.13. Assume that the behavior of each student is independent of the behavior of the other students. Determine the minimum number of students in the class to insure the probability that a blunder is corrected is at least 0.98.

93. Consider Problem 92. Suppose there are four students in the class. Determine the probability that (a) exactly two students recognize a blunder; (b) exactly one student recognizes each of three blunders; (c) the same student recognizes each of three blunders;

(d) two students recognize the first blunder, one student recognizes the second blunder, and no students recognize the third blunder.

105

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106BASIC PROBABILITY THEORY FOR BIOMEDICAL ENGINEERS

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