Answer:
a) The mean of the probability distribution = 0.6
b) The variance of the probability distribution = 0.3
c) The standard deviation of the probability distribution = 0.5
Step-by-step explanation:
a) Data and Calculations:
number of dogs per household in a small town
Dogs Probability Expected Mean Diff Mean Diff.
Value Squared
0 0.650 0 -0.569 0.32376
1 0.216 0.216 -0.353 0.12461
2 0.087 0.174 -0.395 0.15603
3 0.026 0.078 -0.491 0.24108
4 0.014 0.056 -0.513 0.26317
5 0.009 0.045 -0.524 0.27458
The mean = 0.569 (Sum of expected value)
Variance = mean of squared differences = 0.27665 (1.38323/5)
Standard deviation = square root of variance = 0.526 = 0.5
We are given our function as
For finding concavity , firstly we will find second derivative
now, we can find derivative again
now, we can know second derivative is undefined when denominator =0
so, we set denominator =0
and then we can solve for x
now, we can draw a number line and locate x=-4
and then we can find sign of second derivative on each intervals
so,
Concave downward interval:
A variable is just a letter or symbol that symbolizes a number
Therefore, B. 6x is a number multiplied by a letter (product).
