Concept explainers
a)
To show that P(X=0) =
a)
Answer to Problem 29E
P(X=0) =
Explanation of Solution
Given:
X be the
Calculation:
Let, Probability mass
Therefore, just put
b)
To explain why X=0 is same as T>1
b)
Answer to Problem 29E
X=0 is same as T>1
Explanation of Solution
Given:
X be the event that occurs in a 1-second interval.
Calculation:
Here, X=0 mean there are no events occurred in 1 second. That is, the amount of time that elapses until the next event will be greater than 1.
That’s why X=0 is same as T>1.
c)
To show that P(X=0) is same as P(T>1)
c)
Answer to Problem 29E
P(X=0)= P(T>1)
Explanation of Solution
Given:
X be the event that occurs in a 1-second interval.
Calculation:
Here, X=0 mean there are no events occurred in 1 second. That is, the amount of time that elapses until the next event will be greater than 1.
Therefore, P(X=0) =
And P(T>1)=
Both are same.
d)
To show that P(X=0) =
d)
Answer to Problem 29E
P(X=0) =
Explanation of Solution
Given:
X be the event that occurs in a 2-second interval.
Calculation:
Let, Probability mass function of Poisson distribution is,
Therefore, just put
e)
To explain why X=0 is same as T>2
e)
Answer to Problem 29E
X=0 is same as T>2
Explanation of Solution
Given:
X be the event that occurs in a 2-second interval.
Calculation:
Here, X=0 mean there are no events occurred in 2 second. That is, the amount of time that elapses until the next event will be greater than 2.
That’s why X=0 is same as T>2.
f)
To show that P(X=0) =
f)
Answer to Problem 29E
P(X=0) =
Explanation of Solution
Given:
X be the event that occurs in a t-second interval.
Calculation:
Let, Probability mass function of Poisson distribution is,
Therefore, just put x=0 in above formula,
g)
To explain why X=0 is same as T>t
g)
Answer to Problem 29E
X=0 is same as T>t
Explanation of Solution
Given:
X be the event that occurs in a t-second interval.
Calculation:
Here, X=0 mean there are no events occurred in t second. That is, the amount of time that elapses until the next event will be greater than t.
That’s why X=0 is same as T>t.
h)
To show that P(X=0) is same as P(T>t)
h)
Answer to Problem 29E
P(X=0) = P(T>1)
Explanation of Solution
Given:
X be the event that occurs in a t-second interval.
Calculation:
Here, X=0 mean there are no events occurred in 1 second. That is, the amount of time that elapses until the next event will be greater than 1.
Therefore, P(X=0) =
And P(T>t)=
Both are same.
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Chapter 6 Solutions
Elementary Statistics ( 3rd International Edition ) Isbn:9781260092561
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