Suppose that the number of customers who enter a post office in a 49-minute period is a Poisson random variable and that P(X = 0) = 0.03. Determine the (a) mean and (b) variance of X. Round your answers to two decimal places (e. g. 98.76).

Both the mean and the variance are equal to 3.51

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

In which

x is the number of sucesses

is the Euler number

is the mean in the given time interval.

The mean and the variance are equal, so is also the variance.

We have that:

So

Applying ln to both sides

Multiplying by -1

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4

for me what is finding a good play list and going out because i can not lay down and relax so i usually go to a coffee shop. i also use the gum trick and this actually works. another advice is highlighting subjects it really does me remember certain things

step-by-step explanation: