Answer:
a) The probability that the airline will lose no bags next monday is 0.1108
b) The probability that the airline will lose 0,1, or 2 bags next Monday is 0.6227
c) I would recommend taking a Poisson model with mean 4.4 instead of a Poisson model with mean 2.2
Step-by-step explanation:
The probability mass function of X, for which we denote the amount of bags lost next monday is given by this formula

a)

The probability that the airline will lose no bags next monday is 0.1108.
b) Note that
. And

Therefore, the probability that the airline will lose 0,1, or 2 bags next Monday is 0.6227.
c) If the double of flights are taken, then you at least should expect to loose a similar proportion in bags, because you will have more chances for a bag to be lost. WIth this in mind, we can correctly think that the average amount of bags that will be lost each day will double. Thus, i would double the mean of the Poisson model, in other words, i would take a Poisson model with mean 4.4, instead of 2.2.
Rearrange the ODE as


Take

, so that

.
Supposing that

, we have

, from which it follows that


So we can write the ODE as

which is linear in

. Multiplying both sides by

, we have

![\dfrac{\mathrm d}{\mathrm dx}\bigg[e^{x^2}u\bigg]=x^3e^{x^2}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dx%7D%5Cbigg%5Be%5E%7Bx%5E2%7Du%5Cbigg%5D%3Dx%5E3e%5E%7Bx%5E2%7D)
Integrate both sides with respect to

:
![\displaystyle\int\frac{\mathrm d}{\mathrm dx}\bigg[e^{x^2}u\bigg]\,\mathrm dx=\int x^3e^{x^2}\,\mathrm dx](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cint%5Cfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dx%7D%5Cbigg%5Be%5E%7Bx%5E2%7Du%5Cbigg%5D%5C%2C%5Cmathrm%20dx%3D%5Cint%20x%5E3e%5E%7Bx%5E2%7D%5C%2C%5Cmathrm%20dx)

Substitute

, so that

. Then

Integrate the right hand side by parts using



You should end up with



and provided that we restrict

, we can write
513/2=256.5
which means 256 and 257 are the answers
Answer:
h(x) * s(x) = 200(1.05)^(x - 1)
Step-by-step explanation:
Our interest equation is s(x) = (1.05)^(x - 1). This is actually a part of a bigger formula for calculating the amount of money accumulated including interest:
A = P(1 + r)^n, where A is the total, P is the principal amount (initial amount), r is the interest rate, and n is the time
Here, we technically already have the (1 + r)^n part; it's just (1.05)^(x - 1). The principle, though, will actually be the 200 because she starts out at $200.
Thus, to combine these, we simply multiply them together to get:
h(x) * s(x) = 200(1.05)^(x - 1)