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Answer:
b. As the sample size â increases, the variance of decreases. â So, the distribution of becomes highly concentrated around.
Step-by-step explanation:
Let : Yi,.... Yn are = i.i.d are random variables. The probability density of the distribution varies along with the sample size. When the sample size changes, the probability density of also changes.
The probability distribution may be defined as the statistical expression which defines the likelihood of any outcome for the discrete random variable and it can be opposed to the continuous random variable.
In the context, when the size of the sample of the distribution size increases, it causes a decrease in the variance and so the distribution becomes highly concentrated around.
Answer:
(a)Initial Number of Bacteria=600
(b)
Step-by-step explanation:
Given an initial number of bacteria in a petri dish, and each bacteria splits into 2 bacteria after one day.
The function models the number of bacteria, b after d days.
<u>Part A</u>
Given
When d=0,
The initial number of bacteria in the petri dish,
<u>Part B</u>
After 5 days, when d=5
9514 1404 393
Answer:
- relative minimum -6√3 at x = -√3
- relative maximum 6√3 at x = √3
- decreasing on x < -√3 and x > √3
- increasing on -√3 < x < √3
- see below for a graph
Step-by-step explanation:
I find it convenient to draw the graph first when looking for relative extrema.
The function can be differentiated to get ...
f'(x) = -3x^2 +9
This is zero when ...
-3x^2 +9 = 0
x^2 = 3
x = ±√3 . . . . . x-values of relative extrema
Then the extreme values are ...
f(±√3) = x(9 -x^2) = (±√3)(9 -3) = ±6√3
The lower extreme (minimum) corresponds to the lower value of x (-√3), so the extrema are ...
(x, y) = (-√3, -6√3) and (√3, 6√3)
__
Since the leading coefficient is negative and the degree is odd, the function is decreasing for values of x below the minimum and above the maximum. It is increasing for values of x between the minimum and the maximum.
decreasing: x < -√3, and √3 < x
increasing: -√3 < x < √3
