Answer:
y intercept = 3
--- slope
Step-by-step explanation:
Given
The attached graph
Required
Determine the slope and the y intercept
The is at the point where
.
From the graph:
Hence,
y intercept = 3
Next, we calculate the slope using:
Where:
So, we have:
Answer:
a)
b)
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 "life lengths of automobile tires of a certain brand" and we know that the distribution is given by:
The cumulative distribution function is given by:
Part a
We want to find this probability:
and for this case we can use the cumulative distribution function to find it like this:
Part b
For this case w want to find this probability
We have an important property on the exponential distribution called "Memoryless" property and says this:
On this case if we use this property we have this:
We can use the definition of the density function and find this probability:
For this case we have that by definition of properties of powers and roots, it is fulfilled that:
So:
So, we have to:
Answer:
Option B