An information source generates symbols at random from a four-letter alphabet {a,b,c,d} with probabilities P(a) = 1/2, P(b) = 1/4, P(c) = P(d) = 1/8. A coding scheme encodes these symbols into binary codes as follows: a b 10 110 d. 111 Let X be the random variable denoting the lenght of the code, that is the number of binary symbols. Assuming that the generations of symbols are independent, please find E(X²) =? O a. 11/16 O b. 2 Oc. 9/4 O d. 7/4 е. 15/4

College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter9: Counting And Probability
Section9.2: Probability
Problem 31E
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An information source generates symbols at random from a four-letter alphabet {a,b,c,d} with
probabilities P(a) = 1/2, P(b) = 1/4, P(c) = P(d) = 1/8. A coding scheme encodes these
symbols into binary codes as follows:
a
b
10
110
d
111
Let X be the random variable denoting the lenght of the code, that is the number of binary
symbols. Assuming that the generations of symbols are independent, please find E(X2) =?
O a. 11/16
O b. 2
O c. 9/4
O d. 7/4
е. 15/4
Transcribed Image Text:An information source generates symbols at random from a four-letter alphabet {a,b,c,d} with probabilities P(a) = 1/2, P(b) = 1/4, P(c) = P(d) = 1/8. A coding scheme encodes these symbols into binary codes as follows: a b 10 110 d 111 Let X be the random variable denoting the lenght of the code, that is the number of binary symbols. Assuming that the generations of symbols are independent, please find E(X2) =? O a. 11/16 O b. 2 O c. 9/4 O d. 7/4 е. 15/4
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