Mathematics, 24.12.2019 22:31 megababe04

The median of a probability distribution can be defined as the number m such that upper p (upper x less than or equals m )equals upper p (upper x greater than or equals m ). find an expression for the median m of the exponential distribution.

Answers: 3

Show answers

Answers

Answer from: connorgrabski51

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 $\beta$ for some $\beta \in R 0$ "

Then the median of X is $\beta ln (2)$

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:

$f_X (x) = \frac{1}{\beta} e^{-\frac{x}{\beta}}$

Since we need the median we can put this equation:

P(X

If we evaluate the integral we got this:

$\frac{1}{\beta} \int_0^M e^{- \frac{x}{\beta}}dx =\frac{1}{\beta} [-\beta e^{-\frac{x}{\beta}}] \Big|_0^M$

And that's equal to:

$1/2 = 1 -e^{- \frac{M}{\beta}}$

And if we solve for M we got:

$1-e^{- \frac{M}{\beta}} = \frac{1}{2}$

$e^{- \frac{M}{\beta}}=\frac{1}{2}$

If we apply natural log on both sides we got:

$-\frac{M}{\beta}=ln(1/2)$

And then $M=\beta ln(2)$

Answer from: Quest

a) one student is chosen from classroom a, then a student is chosen from classroom b.

step-by-step explanation:

independent events are ones in which the probability of one event does not affect the probability of the second event.

one student is chosen from classroom a; this does not affect the chances of choosing a student from classroom b. this makes these independent events.

when one card is chosen from a standard deck and then set aside before a second card is chosen, the probability of the second card being chosen changes. this makes them dependent events.

when one student is chosen from classroom a and then a second student is chosen from classroom a, the probability of choosing the second student changes. this makes them dependent events.

when a letter is chosen from the alphabet and then a second letter is chosen, the probability of choosing the second letter changes. this makes them dependent events.

Answer from: Quest

i dont know nkw

step-by-step explanation:

kenffledkedncklzkdfeserw

Another question on Mathematics

Mathematics, 21.06.2019 15:10

What is the equation of the graph below? y=sec(x)-4

Answers: 3

Answer

Mathematics, 22.06.2019 01:00

70 points ! pls 2. given the following two sets of data what is the union of the two sets and what is the intersection of the two sets. set a = {1, 2, 3, 4, 5, 6, 7, 8, 9} set b = {2, 4, 6, 8, 10, 12, 14} 3. given a regular deck of cards. describe a way of pulling cards that would create a dependent event and then one that would create an independent event. 4. what is the probability of drawing a red card and then drawing a spade without replacing the card that was drawn first?

Answers: 1

Answer

Mathematics, 22.06.2019 05:30

Given: df and de are midsegments of abc prove: de=1/2 ac

Answers: 1

Answer

Mathematics, 22.06.2019 06:00

How many points must you create to draw a line a segment or a ray

Answers: 1

Answer

You know the right answer?

The median of a probability distribution can be defined as the number m such that upper p (upper x l...