How to do this problem 2 + 1/8

An exponential random variable has a standard deviation of 16. Calculate The probability that it takes on a value < 11. Use 3

antiseptic1488 [7]

Answer:

$P(X$

And using the cdf we got:

$P(X$

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). It is a particular case of the gamma distribution". The probability density function is given by:

$P(X=x)=\lambda e^{-\lambda x}, x>0$

And 0 for other case. Let X the random variable that represent the random variable of interest and we know that the distribution is given by:

$X \sim Exp(\lambda)$

We know the variance on this case given by :

$Var(X) = \frac{1}{\lambda^2}$

So then the deviation is given by:

$Sd(X) = \frac{1}{\sqrt{\lambda}}$

And if we solve for $\lambda$ we got:

$\lambda = (\frac{1}{16})^2 = \frac{1}{256}$

The cumulative distribution function for the exponential distribution is given by:

$F(x) = 1- e^{-\lambda x}$

Solution to the problem

And for this case we want to find this probability:

$P(X$

And using the cdf we got:

$P(X$

5 0

3 years ago

The base of a pyramid has n sides. write an expression for the number of corners on the pyramid.

melisa1 [442]

Answer:

n+1

If a pyramid has n number of sides

⇒number of vertices in the base = n

Since in a pyramid there is one vertex on the top,and n number of faces are on the sides,and one face is in the base.

Total number of faces of pyramid = n+1

7 0

3 years ago

Suppose that the perimeter a rectangle is 54 feet, and the length is 13 feet more than the width. Find the width ractangle, in f

Vesnalui [34]

Answer:7feet

Step-by-step explanation:

perimeter(p)=54ft

Width(w) +13=Length(L)

Perimeter=2xLength+2xwidth

P=2xL+2xw

L=w+13

54=2(w+13)+2w

54=2w+26+2w

Collect like terms

54-26=2w+2w

28=4w

Divide both sides by 4

28/4=4w/4

7=w

Width =7feet

8 0

3 years ago

For a certain river, suppose the drought length Y is the number of consecutive time intervals in which the water supply remains

AnnZ [28]

Answer:

a) There is a 9% probability that a drought lasts exactly 3 intervals.

There is an 85.5% probability that a drought lasts at most 3 intervals.

b)There is a 14.5% probability that the length of a drought exceeds its mean value by at least one standard deviation

Step-by-step explanation:

The geometric distribution is the number of failures expected before you get a success in a series of Bernoulli trials.

It has the following probability density formula:

$f(x) = (1-p)^{x}p$

In which p is the probability of a success.

The mean of the geometric distribution is given by the following formula:

$\mu = \frac{1-p}{p}$

The standard deviation of the geometric distribution is given by the following formula:

$\sigma = \sqrt{\frac{1-p}{p^{2}}$

In this problem, we have that:

$p = 0.383$

So

$\mu = \frac{1-p}{p} = \frac{1-0.383}{0.383} = 1.61$

$\sigma = \sqrt{\frac{1-p}{p^{2}}} = \sqrt{\frac{1-0.383}{(0.383)^{2}}} = 2.05$

(a) What is the probability that a drought lasts exactly 3 intervals?

This is $f(3)$

$f(x) = (1-p)^{x}p$

$f(3) = (1-0.383)^{3}*(0.383)$

$f(3) = 0.09$

There is a 9% probability that a drought lasts exactly 3 intervals.

At most 3 intervals?

This is $P = f(0) + f(1) + f(2) + f(3)$

$f(x) = (1-p)^{x}p$

$f(0) = (1-0.383)^{0}*(0.383) = 0.383$

$f(1) = (1-0.383)^{1}*(0.383) = 0.236$

$f(2) = (1-0.383)^{2}*(0.383) = 0.146$

Previously in this exercise, we found that $f(3) = 0.09$

So

$P = f(0) + f(1) + f(2) + f(3) = 0.383 + 0.236 + 0.146 + 0.09 = 0.855$

There is an 85.5% probability that a drought lasts at most 3 intervals.

(b) What is the probability that the length of a drought exceeds its mean value by at least one standard deviation?

This is $P(X \geq \mu+\sigma) = P(X \geq 1.61 + 2.05) = P(X \geq 3.66) = P(X \geq 4)$ .

We are working with discrete data, so 3.66 is rounded up to 4.

Either a drought lasts at least four months, or it lasts at most thee. In a), we found that the probability that it lasts at most 3 months is 0.855. The sum of these probabilities is decimal 1. So:

$P(X \leq 3) + P(X \geq 4) = 1$