Solution Found!
Solved: Suppose that the random variable X has a geometric
Chapter 3, Problem 120E(choose chapter or problem)
Suppose that the random variable X has a geometric distribution with a mean of 2.5. Determine the following probabilities:
(a) \(P(X=1)\) (b) \(P(X=4)\) (c) \(P(X=5)\)
(d) \(P(X \leq 3)\) (e) \(P(X>3)\)
Equation transcription:
Text transcription:
P(X=1)
P(X=4)
P(X=5)
P(X \leq 3)
P(X>3)
Questions & Answers
QUESTION:
Suppose that the random variable X has a geometric distribution with a mean of 2.5. Determine the following probabilities:
(a) \(P(X=1)\) (b) \(P(X=4)\) (c) \(P(X=5)\)
(d) \(P(X \leq 3)\) (e) \(P(X>3)\)
Equation transcription:
Text transcription:
P(X=1)
P(X=4)
P(X=5)
P(X \leq 3)
P(X>3)
ANSWER:Solution :
Step 1 of 5:
Let X be a random variable has a geometric distribution with of mean of 2.5.
Given geometric distribution,
Then,
Therefore, p=0.4.
Then (1-p) is
1-p = 1-0.4
1-p = 0.6
Hence, 1-p=0.6.
The formula for the geometric distribution is
P(X=x) =
Where p=0.4 and 1-p=0.6.
Our goal is:
We need to find the following probabilities:
a). P(X=1).
b). P(X=4).
c). P(X=5).
d). P(X3).
e). P(X>3).
a). Given P(X=1).
P(X=1) =
P(X=1) =
P(X=1) =
P(X=1) = 0.4
Therefore, P(X=1) = 0.4.