The exponential distribution is frequently applied to the waiting times between successes in a poisson process. if the number of calls received per hour by a telephone answering service is a poisson random variable with parameter î» = 6, we know that the time, in hours, between successive calls has an exponential distribution with parameter î² =1/6. what is the probability of waiting more than 15 minutes between any two successive calls?

P(x>15) = 0.9656

Step-by-step explanation:

No. of calls received is a poisson random variable with parameter = 6

mean = 6

And the waiting time between the phone calls received is exponentially distributed with parameter m = 1\6.

We need to find the waiting time more than 15 minutes.

1hour= 60 minutes

15 minutes= 0.214 hours.

P(x>x) = e^{-mx)

P(x>0.214) = e^{-0.214\6}

                 = 0.9656

d

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.

y=1/4x-4

step-by-step explanation: