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Answer:
a) time=
b)
c)
Step-by-step explanation:
Definitions and concepts
The Poisson process is useful when we want to analyze the probability of ocurrence of an event in a time specified. The probability distribution for a random variable X following the Poisson distribution is given by:
And the parameter represent the average ocurrence rate per unit of time.
The exponential distribution is useful when we want to describ the waiting time between Poisson occurrences. If we assume that the random variable T represent the waiting time btween two consecutive event, we can define the probability that 0 events occurs between the start and a time t, like this:
a. What is the expected time you would have to wait to see ten birds arrive?
The original rate for the Poisson process is given by the problem "rate of six per hour" and on this case since we want the expected waiting time for 10 birds we have this:
time=
b. What is the probability that the elapsed time between the second and third birds exceeds fifteen minutes?
Assuming that the time between the arrival of two birds consecutive follows th exponential distribution and we need that this time exceeds fifteen minutes. If we convert the 15 minutes to hours we have 15(1/60)=0.25 hours. And we want to find this probability:
And we can use the result obtained from the definitions and we have this:
c. If you have already waited five minutes for the first bird to arrive, what is the probability that the bird will arrive within the next five minutes?
First we need to convert the 5 minutes to hours and we got 5(1/60)=0.0833h. And on this case we want a conditional probability. And for this case is good to remember the "Markovian property of the Exponential distribution", given by :
Since we have a waiting time for the first bird of 5 min = 0.0833h and we want that the next bird will arrive within 5 minutes=0.0833h, we can express on this way the probability of interest:
And using the Markovian property we have this:
Step-by-step explanation:
We are to get the expression for the following statements;
1) The difference of nine times a number x and the quotient of that number and 5.
The product of nine and a number x is expressed as;
The quotient of that number and 5.
The difference between both expression;
Hence, the difference of nine times a number x and the quotient of that number and 5 is expressed as
2) Eight more than the quotient of twelve and a number n
Quotient of twelve and a number n is expressed as:
Eight more than the resulting function is;
Hence eight more than the quotient of twelve and a number n is expressed as
3) The product of a number and the quantity 'six minus the number' plus the quotient of eight and the number.
Let the number be x:
six minus the number is expressed as;
product of a number x and the quantity 'six minus the number is;
quotient of eight and the number is;
Taking the resulting sum of the last two expression
Hence the product of a number and the quantity 'six minus the number' plus the quotient of eight and the number is expressed as;
4) Sum of three consecutive even integers. 2x + (2x + 2) + (2x + 4).
Let the first even number be 2x
The consecutive even numbers are gotten by adding 2 to the preceding number. The two consecutive even integers are 2x+2 and 2x+2+2
the sum of three consecutive even integers is expressed as;
<h3>Answer:</h3>
The rules of exponents tell you ...
... (a^b)(a^c) = a^(b+c) . . . . . . applies inside parentheses
... (a^b)^c = a^(b·c) . . . . . . . . applies to the overall expression
The Order of Operations tells you to evaluate inside parentheses first. Doing that, you have ...
... x^(4/3)·x^(2/3) = x^((4+2)/3) = x^2
Now, you have ...
... (x^2)^(1/3)
and the rule of exponents tells you to multiply the exponents.
... = x^(2·1/3) = x^(2/3)