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Raymond has a motion detector light which gets activated an average of 15 times every 2 hours during the night. In order to find the probability that the motion detector light will be activated exactly 8 times in a 55 minute period during the night using the Poisson distribution, what does the random variable X represent

Sagot :

Melissacastr02442

Answer:

The random variable X is the number of activations that occur in the 55 minute time period.

Step-by-step explanation:

The random variable X represents the number of occurrences of an event in the time interval of interest. The time interval of interest is the fixed time period for which the probability of an event is being sought. In this case, the time interval of interest is 55 minutes. The random variable X is the number of activations that occur in the 55 minute time period.

anuksha0456

In the given Poisson Distribution, the random variable X represents the number of activation in 55 minutes. Hence, the 4th option is the right choice.

What is Poisson Distribution?

A Poisson distribution is a probability distribution used in statistics to illustrate how many times an event is expected to occur over a certain time period. It is, in other words, a count distribution. Poisson distributions are frequently used to analyze independent events that occur at a consistent rate during a specified time frame. It was named after Siméon Denis Poisson, a French mathematician.

The Poisson distribution is a discrete function, which means that the variable may only take values from a (possibly endless) list. To put it another way, the variable cannot accept all values in any continuous range. The variable in the Poisson distribution may only take whole integer values (0, 1, 2, 3, etc.), no fractions or decimals.

How to solve the question?

In the question, we are informed that Raymond has a motion detector light that gets activated an average of 15 times every 2 hours during the night.

We are asked what the random variable X represents, to find the probability that the motion detector light will be activated exactly 8 times in 55 minutes during the night using the Poisson distribution.

The formula for the Poisson Distribution is given as,

[tex]P(X = x) = e^{-\lambda}\frac{\lambda^x}{x!}[/tex]

where e is the Euler's number, x is the number of occurrence, and λ is the expected value.

The term X is the variable over which the distribution is defined.

Thus, in the given Poisson Distribution, the random variable X represents the number of activation in 55 minutes. Hence, the 4th option is the right choice.

Learn more about Poisson Distribution at

https://brainly.com/question/16795264

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Refer to the attachment for the complete question.

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