Please show and explain the steps! Solve only (a), (b), and (c)!
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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Please show and explain the steps! Solve only (a), (b), and (c)!
![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).
X1
1
2
P(x,) | 0.4 0.2 0.4
u = 1, o2 = 0.8
(a) Determine the pmf of T, = X, + X2.
to
1
3
4
P(t,)
(b) Calculate uT
How does it relate to u, the population mean?
2
(c) Calculate
How does it relate to o?, the population variance?
2
g2
(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. Wwith T, = the sum of all four X,'s, what now are the values of E(T) and V(T,)?
E(T,) =
V(T.) =
(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) =
P(T, 2 7) =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc32f563a-6b55-4123-a4c3-1254c39a7403%2F224a505d-760c-423a-bd27-4db1771987d3%2Frf3oskr_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).
X1
1
2
P(x,) | 0.4 0.2 0.4
u = 1, o2 = 0.8
(a) Determine the pmf of T, = X, + X2.
to
1
3
4
P(t,)
(b) Calculate uT
How does it relate to u, the population mean?
2
(c) Calculate
How does it relate to o?, the population variance?
2
g2
(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. Wwith T, = the sum of all four X,'s, what now are the values of E(T) and V(T,)?
E(T,) =
V(T.) =
(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) =
P(T, 2 7) =
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