Answer:
c) 2
d) 0.96
Step-by-step explanation:
We are given the following in the question:
a) probability density function.
![\displaystyle\int^{\infty}_{\infty}f(x) dx = 1\\\\\displaystyle\int^{\infty}_{-\infty}2x^{-3}dx = 1\\\\\displaystyle\int^{\infty}_{1}2x^{-3}dx\\\\\Rightarrow \big[-x^{-2}\big]^{\infty}_1\\\\\Rightarrow -(0-1) = 1](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cint%5E%7B%5Cinfty%7D_%7B%5Cinfty%7Df%28x%29%20dx%20%3D%201%5C%5C%5C%5C%5Cdisplaystyle%5Cint%5E%7B%5Cinfty%7D_%7B-%5Cinfty%7D2x%5E%7B-3%7Ddx%20%3D%201%5C%5C%5C%5C%5Cdisplaystyle%5Cint%5E%7B%5Cinfty%7D_%7B1%7D2x%5E%7B-3%7Ddx%5C%5C%5C%5C%5CRightarrow%20%5Cbig%5B-x%5E%7B-2%7D%5Cbig%5D%5E%7B%5Cinfty%7D_1%5C%5C%5C%5C%5CRightarrow%20-%280-1%29%20%3D%201)
Thus, it is a probability density function.
b) cumulative distribution function.
c) mean of the distribution
d) probability that the size of random particle will be less than 5 micrometers
A) True. The domain of both is: x ≥ 0
B) True. 1/2 is on the outside so it is vertical. 1/2 is between 0 and 1 so it shrinks.
C) False. the coefficient is not 2 (it is 1/2)
D) False. 1/2 is not on the inside with "x" so it is not horizontal.
Answer: A, B
Answer:
389.9 to 1 decimal place
If you need another explanation comment on this one
Answer:
0.000002
Step-by-step explanation:
2* 10^-6
is the same as
2 * 0.000001
which is
0.000002
-9 because a negative plus a negative is a negative so -5+-4 or -5-4 is -9
