3.2 . I don't really know how to explain this, but I need to write at least 20 characters to give you my answer.
Answer:
tex]M=\beta ln(2)[/tex]
Step-by-step explanation:
Previous concepts
The exponential distribution is "the probability distribution of the time between events in a Poisson process (a process in which events occur continuously and independently at a constant average rate).
Solution to the problem
For this case we can use the following Theorem:
"If X is a continuos random variable of the exponential distribution with parameter 
for some 
"
Then the median of X is 
Proof
Let M the median for the random variable X.
From the definition for the exponential distribution we know the denisty function of X is given by:
Since we need the median we can put this equation:
If we evaluate the integral we got this:
![\frac{1}{\beta} \int_0^M e^{- \frac{x}{\beta}}dx =\frac{1}{\beta} [-\beta e^{-\frac{x}{\beta}}] \Big|_0^M](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B%5Cbeta%7D%20%5Cint_0%5EM%20e%5E%7B-%20%5Cfrac%7Bx%7D%7B%5Cbeta%7D%7Ddx%20%3D%5Cfrac%7B1%7D%7B%5Cbeta%7D%20%5B-%5Cbeta%20e%5E%7B-%5Cfrac%7Bx%7D%7B%5Cbeta%7D%7D%5D%20%5CBig%7C_0%5EM)
And that's equal to:
And if we solve for M we got:
If we apply natural log on both sides we got:
And then 
Answer:
Suppose that you have 50 people that like hip hop and 50 people that like country.
Now, the union of those sets would be 50 + 50 = 100 people, right?
Well, this may be incorrect, because in the 50 people that like hip hop, we may have, for example, 10, that also like country (this means that in the 50 people that like country, we also have 10 that like hip hop).
Then when we are adding 50 + 50 we are counting those 10 people in both groups, and that is why the direct addition may be different than the union of both sets.
In more technical words, the union of two sets is equal to the addition of the elements of both sets minus the elements in the intersection of both sets (in our prior example, the 10 people that like hip hop and country music are the intersection of both sets)
Answer:
Linear
Step-by-step explanation:
"−5x − 7 < −22 and −5x − 7 greater than or equal to −3" is the one among the following choices given in the question that is <span>an equivalent form of the compound inequality −22 > −5x − 7 greater than or equal to −3. The correct option among all the options that are given in the question is option "A" or the first option.</span>
