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There are two traffic lights on a commuter’s route to and from work. Let X 1 be the number of lights at which the commuter must stop on his way to work, and X 2 be the number of lights at which he must stop when returning from work. Suppose these two variables are independent, each with pmf given in the accompanying table (so X 1 , X 2 is a random sample of size n = 2). x 1 0 1 2 p ( x 1 ) 0.2 0.5 0.3 µ =1.1, σ 2 =0.49 a. Determine the pmf of T o = X 1 + X 2 . b. Calculate µT o . How does it relate to µ , the population mean? c. Calculate σ 2 T o . How does it relate to σ 2 , the population variance? d. Let X 3 and X 4 be the number of lights at which a stop is required when driving to and from work on a second day assumed independent of the first day. With T o = the sum of all four X i ’s, what now are the values of E ( T o ) and V ( T o )? e. Referring back to (d), what are the values of P ( T 0 = 8) and P ( T o ≥ 7) [ Hint : Don’t even think of listing all possible outcomes!]

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Probability and Statistics for Eng...

9th Edition
Jay L. Devore
Publisher: Cengage Learning
ISBN: 9781305251809
BuyFind

Probability and Statistics for Eng...

9th Edition
Jay L. Devore
Publisher: Cengage Learning
ISBN: 9781305251809

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Chapter
Section
Chapter 5.3, Problem 38E
Textbook Problem

There are two traffic lights on a commuter’s route to and from work. Let X1 be the number of lights at which the commuter must stop on his way to work, and X2 be the number of lights at which he must stop when returning from work. Suppose these two variables are independent, each with pmf given in the accompanying table (so X1, X2 is a random sample of size n = 2).

x1 0 1 2
p(x1) 0.2 0.5 0.3

    µ =1.1, σ2=0.49

  1. a. Determine the pmf of To = X1 + X2.
  2. b. Calculate µTo. How does it relate to µ, the population mean?
  3. c. Calculate σ2 To. How does it relate to σ2, the population variance?
  4. d. Let X3 and X4 be the number of lights at which a stop is required when driving to and from work on a second day assumed independent of the first day. With To = the sum of all four Xi’s, what now are the values of E(To) and V(To)?
  5. e. Referring back to (d), what are the values of P(T0 = 8) and P(To ≥ 7) [Hint: Don’t even think of listing all possible outcomes!]

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Chapter 5 Solutions

Probability and Statistics for Engineering and the Sciences
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