There are two traffic lights on a commuter's route to and from work. Let X, be the number of lights at which the commuter must stop on his way to work, and X, be the number of lights at which he must stop when returning from work. Suppose that these two variables are Independent, each with the pmf given in the accompanying table (so X,, X, is a random sample of size n= 2). P(x,) 0.3 0.4 0.3 - 1, o? - 0.6 (a) Determine the pmf of T,- X, + X. to 1 2 p(t,) 0.09V 0.24 0.34 V 0.24 V 0.09 (b) Calculate T HT, - 2 How does relate to , the population mean? HT.2 (c) Calculate a. - 2 How does relate to o, the population variance? 2- (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 T, - the sum of all four X's, what now are the values of E(T) and V(T)? E(T) - 4 V(T) - 24 (e) Referring back to (d), what are the values of P(T, - 8) and P(T, 2 7) (Hint: Don't even think of listing all possible outcomes!] P(T, - 8) - 0.0081 P(T, 2 7) - 0.0405
There are two traffic lights on a commuter's route to and from work. Let X, be the number of lights at which the commuter must stop on his way to work, and X, be the number of lights at which he must stop when returning from work. Suppose that these two variables are Independent, each with the pmf given in the accompanying table (so X,, X, is a random sample of size n= 2). P(x,) 0.3 0.4 0.3 - 1, o? - 0.6 (a) Determine the pmf of T,- X, + X. to 1 2 p(t,) 0.09V 0.24 0.34 V 0.24 V 0.09 (b) Calculate T HT, - 2 How does relate to , the population mean? HT.2 (c) Calculate a. - 2 How does relate to o, the population variance? 2- (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 T, - the sum of all four X's, what now are the values of E(T) and V(T)? E(T) - 4 V(T) - 24 (e) Referring back to (d), what are the values of P(T, - 8) and P(T, 2 7) (Hint: Don't even think of listing all possible outcomes!] P(T, - 8) - 0.0081 P(T, 2 7) - 0.0405
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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![There are two traffic lights on a commuter's route to and from work. Let X, be the number of lights at which the commuter must stop on his way to work, and X, be the number of lights at which he must stop when returning from work. Suppose that these two variables are
independent, each with the pmf given in the accompanying table (so X,, X, is a random sample of size n = 2).
1
2
X1
p(x1) 0.3 0.4 0.3
u = 1, o? = 0.6
(a) Determine the pmf of
X1 + X2.
2
3
4
1
to
0.34
0.24
0.09
0.24
p(t,) ||0.09
(b) Calculate
= 2
PT.
How does it relate to u, the population mean?
= 2
PT.
2
(c) Calculate
OT
To
2
%3D
2
OTO
How does it relate to o, the population variance?
2
OTO
= the sum of all four X,'s, what now are the values of E(T) and V(T)?
(d) Let X, and X, 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.
E(T,)
4
V(T,)
2.4
(e) Referring back to (d), what are the values of P(T, = 8) and P(T, 2 7) [Hint: Don't even think of listing all possible outcomes!]
0.0081
P(T, = 8)
0.0405
P(T, > 7)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F86bfc21f-7304-4d6a-8ae3-de059a5180e7%2F29a206fb-7a58-4ba3-b819-fb65c65b2aa6%2Fa8tj6if_processed.png&w=3840&q=75)
Transcribed Image Text:There are two traffic lights on a commuter's route to and from work. Let X, be the number of lights at which the commuter must stop on his way to work, and X, be the number of lights at which he must stop when returning from work. Suppose that these two variables are
independent, each with the pmf given in the accompanying table (so X,, X, is a random sample of size n = 2).
1
2
X1
p(x1) 0.3 0.4 0.3
u = 1, o? = 0.6
(a) Determine the pmf of
X1 + X2.
2
3
4
1
to
0.34
0.24
0.09
0.24
p(t,) ||0.09
(b) Calculate
= 2
PT.
How does it relate to u, the population mean?
= 2
PT.
2
(c) Calculate
OT
To
2
%3D
2
OTO
How does it relate to o, the population variance?
2
OTO
= the sum of all four X,'s, what now are the values of E(T) and V(T)?
(d) Let X, and X, 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.
E(T,)
4
V(T,)
2.4
(e) Referring back to (d), what are the values of P(T, = 8) and P(T, 2 7) [Hint: Don't even think of listing all possible outcomes!]
0.0081
P(T, = 8)
0.0405
P(T, > 7)
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