Asked by Angel Barrancaa on Jun 03, 2024
Verified
Given a Poisson random variable X,where the average number of successes occurring in a specified interval is 1.8,then P(X = 0) is:
A) 1.8
B) 1.3416
C) 0.1653
D) 6.05
Poisson Random Variable
A statistical measure that expresses the probability of a given number of events occurring in a fixed interval of time or space, assuming these events happen with a known constant mean rate and independently of the time since the last event.
Specified Interval
A defined range of values within which a particular parameter or statistic is expected to lie.
- Analyze and calculate probabilities in given situations using the Poisson distribution.
Verified Answer
where λ is the average number of successes occurring in the specified interval
Here, λ = 1.8 and X = 0.
P(X=0) = (e^-1.8 * 1.8^0)/0!
P(X=0) = e^-1.8 = 0.1653 (approx)
Therefore, the correct choice is C.
Learning Objectives
- Analyze and calculate probabilities in given situations using the Poisson distribution.
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