When a curve and a line meet at a point, are their gradient equal?
1 answer:
Check the picture below.
the slope goes by several names
• average rate of change
• rate of change
• deltaY over deltaX
• Δy over Δx
• rise over run
• gradient
• constant of proportionality
however, is the same cat wearing different costumes.
well, by the definition of a derivative, the slope at the point is f'(a), and any tangent line going through it will also have the same exact slope, keeping in mind that a straight line has a constant slope.
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Answer:
a) 0.164 = 16.4% probability that a disk has exactly one missing pulse
b) 0.017 = 1.7% probability that a disk has at least two missing pulses
c) 0.671 = 67.1% probability that neither contains a missing pulse
Step-by-step explanation:
To solve this question, we need to understand the Poisson distribution and the binomial distribution(for item c).
Poisson distribution:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
In which
x is the number of sucesses
is the Euler number
is the mean in the given interval.
Binomial distribution:
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
In which is the number of different combinations of x objects from a set of n elements, given by the following formula.
And p is the probability of X happening.
Poisson mean:
a. What is the probability that a disk has exactly one missing pulse?
One disk, so Poisson.
This is P(X = 1).
0.164 = 16.4% probability that a disk has exactly one missing pulse
b. What is the probability that a disk has at least two missing pulses?
In which
In which
0.017 = 1.7% probability that a disk has at least two missing pulses
c. If two disks are independently selected, what is the probability that neither contains a missing pulse?
Two disks, so binomial with n = 2.
A disk has a 0.819 probability of containing no missing pulse, and a 1 - 0.819 = 0.181 probability of containing a missing pulse, so
We want to find P(X = 0).
0.671 = 67.1% probability that neither contains a missing pulse