Answer:
a. p(orange) = 5/14
b. p(green) = 3/14
c. p(red) = 1/7
d. p(brown) = 2/7
e. p(brown or red) = 3/7
Step-by-step explanation:
1. You have a 14 pencils. Two pencils are red, 5 pencils are orange, 3 pencils are green and 4 pencils are brown.
p(color) = (number of pencils of that color)/(total number of pencils)
p(color) = (number of pencils of that color)/14
a. If a pencil is picked at random, what is the probability that the pencil
will be orange?
p(orange) = 5/14
b. If a pencil is picked at random, what is the probability that the pencil
will be green?
p(green) = 3/14
c. If a pencil is picked at random, what is the probability that the pencil will be red?
p(red) = 2/14 = 1/7
d. If a pencil is picked at random, what is the probability that the pencil
will be brown?
p(brown) = 4/14 = 2/7
e. If a pencil is picked at random, what is the probability that the pencil
will be brown or red?
brown: 4
red: 2
brown or red: 4 + 2
p(brown or red) = 6/14 = 3/7
Answer:

And using the cdf we got:

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:

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:

We know the variance on this case given by :

So then the deviation is given by:

And if we solve for
we got:

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

Solution to the problem
And for this case we want to find this probability:

And using the cdf we got:

Answer:
**The equation is not clear, so I have provided both options**
<h3><u>Option 1</u></h3>


<u>Solution 1</u>



<u>Solution 2</u>




<h3><u>Option 2</u></h3>


<u>Solution 1</u>




<u>Solution 2</u>





Answer:Subtract
from both sides of the equation
from both sides of the equation
Multiply all terms by the same value to eliminate fraction denominators