MHB A. Lahey Electronics: Email Delivery Times & Probabilities

AI Thread Summary
Lahey Electronics conducted an internal study revealing that the mean time for an internal email to arrive is two seconds, following a Poisson distribution. The probability of a message arriving in exactly one second is approximately 0.2707. For messages taking more than four seconds, the probability is about 0.1429. Additionally, the probability of an email arriving in virtually no time, or zero seconds, is approximately 0.1353. These findings highlight the efficiency and reliability of email delivery within the company.
trastic
Messages
4
Reaction score
0
"An internal study at Lahey Electronics,a large software development company,revealed the mean time for an internal email message to arrive at its destination was two seconds. Further, the distribution of the arrival times followed a Poisson distribution.
a.What is the probability a message takes exactly one second to arrive at its destination?
b.What is the probability it takes more than four seconds to arrive at its destination?
c.What is the probability it takes virtually no time, i.e., “zero” seconds?"
 
Mathematics news on Phys.org
I would begin with:

[box=green]
The Poisson Probability Formula

$$P(x)=e^{-\lambda}\frac{\lambda^x}{x!}\tag{1}$$[/box]

In this problem, we are given $$\lambda=2\text{ s}$$.

Can you now use this formula to answer the given questions?
 
Using (1) and $\lambda=2$, we find:

a.What is the probability a message takes exactly one second to arrive at its destination?

$$P(1)=e^{-2}\frac{2^1}{1!}=\frac{2}{e^2}\approx0.270670566473225$$

b.What is the probability it takes more than four seconds to arrive at its destination?

$$P(>4)=1-(P(0)+P(1)+P(2)+P(3)+P(4))=1-\frac{1}{e^2}\left(\frac{2^0}{0!}+\frac{2^1}{1!}+\frac{2^2}{2!}+\frac{2^3}{3!}\right)=1-\frac{1}{e^2}\left(1+2+2+\frac{4}{3}\right)=1-\frac{19}{3e^2}\approx0.142876539501453$$

c.What is the probability it takes virtually no time, i.e., “zero” seconds?"

$$P(0)=e^{-2}\frac{2^0}{0!}=\frac{1}{e^2}\approx0.135335283236613$$
 
Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
Back
Top