Math

StatisticsProbability and Statistics for Engineering and the SciencesThere 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!]BuyFind*arrow_forward*

9th Edition

Jay L. Devore

Publisher: Cengage Learning

ISBN: 9781305251809

Chapter 5.3, Problem 38E

Textbook Problem

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*. How does it relate to_{o}*µ*, the population mean? - c. Calculate
*σ*^{2}*T*. How does it relate to_{o}*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*= the sum of all four_{o}*X*’s, what now are the values of_{i}*E*(*T*) and_{o}*V*(*T*)?_{o} - e. Referring back to (d), what are the values of
*P*(*T*= 8) and_{0}*P*(*T*≥ 7) [_{o}*Hint*: Don’t even think of listing all possible outcomes!]

Probability and Statistics for Engineering and the Sciences

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