![X](https://tex.z-dn.net/?f=X)
has CDF
![F_X(x)=\mathbb P(X\le x)=\begin{cases}1-e^{-\lambda x/2}&\text{for }x\ge0\\0&\text{otherwise}\end{cases}](https://tex.z-dn.net/?f=F_X%28x%29%3D%5Cmathbb%20P%28X%5Cle%20x%29%3D%5Cbegin%7Bcases%7D1-e%5E%7B-%5Clambda%20x%2F2%7D%26%5Ctext%7Bfor%20%7Dx%5Cge0%5C%5C0%26%5Ctext%7Botherwise%7D%5Cend%7Bcases%7D)
The CDF of
![Y](https://tex.z-dn.net/?f=Y)
is then
![F_Y(y)=\mathbb P(Y\le y)=\mathbb P(X^2\le y)=\mathbb P(X\le\sqrt y)=F_X(\sqrt y)](https://tex.z-dn.net/?f=F_Y%28y%29%3D%5Cmathbb%20P%28Y%5Cle%20y%29%3D%5Cmathbb%20P%28X%5E2%5Cle%20y%29%3D%5Cmathbb%20P%28X%5Cle%5Csqrt%20y%29%3DF_X%28%5Csqrt%20y%29)
![\implies F_Y(y)=\begin{cases}1-e^{-\lambda\sqrt y/2}&\text{for }y\ge0\\0&\text{otherwise}\end{cases}](https://tex.z-dn.net/?f=%5Cimplies%20F_Y%28y%29%3D%5Cbegin%7Bcases%7D1-e%5E%7B-%5Clambda%5Csqrt%20y%2F2%7D%26%5Ctext%7Bfor%20%7Dy%5Cge0%5C%5C0%26%5Ctext%7Botherwise%7D%5Cend%7Bcases%7D)
![\implies F_Y(y)=\begin{cases}1-e^{-(y/(4/\lambda^2))^{1/2}}&\text{for }y\ge0\\0&\text{otherwise}\end{cases}](https://tex.z-dn.net/?f=%5Cimplies%20F_Y%28y%29%3D%5Cbegin%7Bcases%7D1-e%5E%7B-%28y%2F%284%2F%5Clambda%5E2%29%29%5E%7B1%2F2%7D%7D%26%5Ctext%7Bfor%20%7Dy%5Cge0%5C%5C0%26%5Ctext%7Botherwise%7D%5Cend%7Bcases%7D)
which is the CDF of a Weibull distribution with shape parameter
![\dfrac4{\lambda^2}](https://tex.z-dn.net/?f=%5Cdfrac4%7B%5Clambda%5E2%7D)
and scale parameter
![\dfrac12](https://tex.z-dn.net/?f=%5Cdfrac12)
.
Answer:
about 5.3
Step-by-step explanation:
12.64*4=50.56-3.50=47.06
47.06+d
It needs permutations of the order does matter, like 3 people ordering from a coffee shop to see who goes first.
Combinations are when the order doesn't matter, like if you had 3 numbers behind your back and you had to guess the 3 not in order
It needs neither when you don't need to find the amount of choices you have (or something similar) for something
Answer:
D. The standard deviation is known and n > 30.
Step-by-step explanation:
- Your sample size is greater than 30.
- Data points should be away from each other.
- Your data should be commonly categorized.
- Your data should be randomly picked from a population. Each item should have an equal chance of being selected.
- The sample sizes should be equal.