Solution Found!
Suppose that Y has a gamma distribution with ? = 3 and ? =
Chapter 4, Problem 180SE(choose chapter or problem)
Suppose that 𝑌 has a gamma distribution with \(\alpha=3\) and \(\beta=1\).
a Use Poisson probabilities to evaluate \(P(Y \leq 4)\). (See Exercise 4.99.)
b Applet Exercise Use the applet Gamma Probabilities and Quantiles to find \(P(Y \leq 4)\).
Equation Transcription:
Text Transcription:
alpha=3
beta=1
P(Y</=4)
P(Y</=4)
Questions & Answers
QUESTION:
Suppose that 𝑌 has a gamma distribution with \(\alpha=3\) and \(\beta=1\).
a Use Poisson probabilities to evaluate \(P(Y \leq 4)\). (See Exercise 4.99.)
b Applet Exercise Use the applet Gamma Probabilities and Quantiles to find \(P(Y \leq 4)\).
Equation Transcription:
Text Transcription:
alpha=3
beta=1
P(Y</=4)
P(Y</=4)
ANSWER:
Solution :
Step 1 of 2:
Let Y has a gamma distribution with =3 and
=2.
Our goal is:
a). We need to use the poisson probability to evaluate P(X4).
b). We use the applet gamma probabilities and quantiles to find P(Y4) .
Now we have to use the poisson probability to evaluate P(X4).
Then the poisson distribution is
P(Yk) =
P(Yk) = P(X
)
Where X is poisson distributed with =1.
The poisson probability formula is
P(X=x) =
Then the probability of Y4 is
P(Y4) =1-
P(Y4) =1-
P(Y4) =1-(0.01831+0.073263+0.146525
P(Y4) = 1-0.2381
P(Y4) = 0.7619
Therefore P(Y4) is 0.7619.