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Suppose that the telephone calls during one minute time follow a Poisson distribution with mean=4. If people can handle at most 6 calls per minute, what is the probability that the people will receive more calls than they can handle during one-minute interval?

Hi,

I am just confused whether this question is conditional probability.

Since people can handle at most 6 calls during one-minute.

Probability of receiving more calls than they can manage is P(X>6), or is it a conditional probability? Given that they can handle at most 6 calls, Probability of receiving more calls than they can manage is P(X>6 given that X<=6) ?

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    $\begingroup$ It does not look like a conditional probability. Just $P(X \gt 6)$ $\endgroup$
    – Henry
    Jan 19, 2015 at 16:18
  • $\begingroup$ The probability you just wrote down is certainly $0$ since if $X\le6$, it is impossible for $X>6$ to occur. $\endgroup$
    – AlexR
    Jan 19, 2015 at 16:18

3 Answers 3

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Looking at this as a conditional probability has no use. You can see that by your last statement:

P(X>6 given that X<=6) is always identically zero; if $X\leq 6$ then $X$ is never greater than 6.

Conditional probabilitiees are a meaningful concept when a problem involves two or more random variates (generally non-independent variates).

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This is just an unconditional probability. As you yourself suggest, you need to calculate $P(X>6)$, which is the probability of getting more than the number of manageable calls in a minute.

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I think this question is about unconditional probability. A conditional version of the problem would have been : "give the probability that the people can't handle all the calls given the fact the phone has already rung 3 times".

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