Consider the following scenarios, where we apply probability to a game of flipping coins. In the game, we flip one coin each rou
1 answer:
You might be interested in
Answer:
Step-by-step explanation:
<u>Definitions</u>
Integer: A whole number that can be positive, negative, or zero.
Consecutive Integers: Integers that follow each other continuously in the order from smallest to largest.
Product: The result of multiplying two of more values together.
Let x be the first integer.
Therefore, to find the consecutive integers, add 1 to each term:
- x
- x + 1
- (x + 1) + 1 = x + 2
Therefore, the product of the first three consecutive integers is:
Answer:
a)
b)
c)
d)
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:
Solution to the problem
For this case we have that X is represented by the following distribution:
Is important to remember that th cumulative distribution for X is given by:
Part a
For this case we want this probability:
And using the cumulative distribution function we have this:
Part b
Since we want the probability that the man exceeds the mean by more than 2 deviations
For this case the mean is given by:
And by properties the deviation is the same value
So then 2 deviations correspond to 2*74.516=149.03
And the want this probability:
And we can find this probability using the complement rule:
Part c
For the median we need to find a value of m such that:
If we use the cumulative distribution function we got:
And if we solve for m we got this:
If we apply natural log on both sides we got:
Part d
For this case we have this equation:
If we apply the cumulative distribution function we got:
If w solve for a we can do this:
Using natural log on btoh sides we got: