24- 1,2,3,4,6,8,12,24
64-1,2,4,8,16,32,64
88-1,2,4,8,11,22,44,88
Here are all the factors.^^
The common factors are 1,2,3,4,6
Hope this helps!
Answer:
Step-by-step explanation:
The model 
, the number of planets found up to time 
, as a Poisson process. So, the has distribution of Poison distribution with parameter 
a)
The mean for a month is, 
per month
![E[N(t)]= \lambda t\\\\=\frac{1}{3}(24)\\\\=8](https://tex.z-dn.net/?f=E%5BN%28t%29%5D%3D%20%5Clambda%20t%5C%5C%5C%5C%3D%5Cfrac%7B1%7D%7B3%7D%3C%2Fp%3E%3Cp%3E%2824%29%5C%5C%5C%5C%3D8)
(Here. t = 24)
For Poisson process mean and variance are same,
![Var[N (t)]= Var[N(24)]\\= E [N (24)]\\=8](https://tex.z-dn.net/?f=Var%5BN%20%28t%29%5D%3D%20Var%5BN%2824%29%5D%5C%5C%3D%20E%20%5BN%20%2824%29%5D%5C%5C%3D8)
(Poisson distribution mean and variance equal)
The standard deviation of the number of planets is,
![\sigma( 24 )] =\sqrt{Var[ N(24)]}=\sqrt{8}= 2.828](https://tex.z-dn.net/?f=%5Csigma%28%2024%20%29%5D%20%3D%5Csqrt%7BVar%5B%20N%2824%29%5D%7D%3D%5Csqrt%7B8%7D%3D%202.828%3C%2Fp%3E%3Cp%3E)
b)
For the Poisson process the intervals between events(finding a new planet) have independent exponential distribution with parameter 
. The sum of 
of these independent exponential has distribution Gamma 
.
From the given information, 
and 
Calculate the expected value.
(Here, 
and 
)
C)
Calculate the probability that she will become eligible for the prize within one year.
Here, 1 year is equal to 12 months.
P(X ≤ 12) = (1/Г (k)λ^k)(x)^(k-1).(e)^(-x/λ)
Hence, the required probability is 0.2149 or 21.49%
Answer:vertical
Step-by-step explanation:
<span>It is because even numbers always have a factor of two, and therefore, larger composite even numbers will have factors of two and other even numbers based around two, such as 4, 8, 16, 32, and so on. On the other hand, numbers which are odd can have factors of 3, 5, and 7 for example, and their numbers based around them(3, 9, 27; 5, 10, 15; 7, 49, 343; and so on). If we look into it, notice how for odd numbers the space between the numbers based around 3, 5, and 7 are increasingly further apart. This is the reason why less large odd integers to have numerous factors. It is because odd numbers cannot have the prime factor 2, this will reduce their factor number. And is is also because even numbers are already divided by 2, this will give them more factors over the odd numbers.</span>
