The area under the graph of the continuous uniform distribution is 1.
a. The probability that the value will be between 5 and 7 is the area between 5 and 7.
b. The probability that the value will be between 2 and 3 is the are between 2 and 3.
c. The mean is given by:
d. The variance is given by:
The standard deviation is:
In rolling a die, there are 6 possible outcomes. Each face is numbered from 1 to 6. The possible combinations of numbers so that their sum is 5 is, 1 - 4, 2 - 3, 3 - 2, 4 - 1. Thus, the answer is that they are four possible outcomes corresponding to the given event.
We have been given the expression to be
Since we need to find the tangent at a point, we will have to find the derivative of as the slope of the tangent at a given point on the curve is always equal to value of the derivative at that point.
Thus, we have to find
We will use the product rule of derivatives to find
Thus, (using the product rule which states that )
Taking the common factors out we get:
Thus, at is given by:
=Slope of the tangent of y at x=4=
Thus,
Now, the equation of the tangent line which passes through and has slope m is given by:
Thus, the equation of the tangent line which passes through and has the slope 185 is
Which can be simplified to
Thus,
This is the required equation of the tangent.