What is the significance of the mean of a probability distribution?
1 answer:
Answer:
Significance of the mean of a probability distribution.
Step-by-step explanation:
- The mean of a probability distribution is the arithmetic average value of a random variable having that distribution.
- For a discrete probability distribution, the mean is given by,
, where P(x) is the probabiliy mass function.
- For a continuous probability distribution, the mean s given by,
, where f(x) is the probability density function.
- Mean is a measure of central location of a random variable.
- It is the weighted average of the values that X can take, with weights given by the probability density function.
- The mean is known as expected value or expectation of X.
- An important consequence of this is that the mean of any symmetric random variable (continuous or discrete) is always on the axis of symmetry of the distribution.
- For a continuous random variable, the mean is always on the axis of symmetry of the probability density function.
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Answer:
B) x units
Step-by-step explanation:
Let quadrilateral KMPT be a rectangle with dimensions 12 units by 8 units. Then its perimeter would be equal to:
Perimeter of a rectangle = 2 (l + b)
where: l is the length = 12 units and b is the breadth = 8 units. So that:
Perimeter of KMPT = 2 (12 + 8)
= 40 units
Dilating KMPT by a scale factor of would create K'M'P'T' of dimensions;
× 12 units by
× 8 units. Thus, the dimensions of K'M'P'T' would be 9 units by 6 units.
Perimeter of K'M'P'T' = 2 (l + b)
= 2(9 + 6)
= 30 units
Comparing the perimeters of KMPT and K'M'P'T', the perimeter of K'M'P'T' would be × perimeter of KMPT.
Therefore, if the perimeter of KMPT is x units, then;
perimeter of K'M'P'T' = * x units
= x units
This is a proof that the angles in a triangle equal 180°:
The top
line (that touches the top of the triangle) is
running parallel
to the base of the triangle.
So:
<span> <span>angles A are the same </span> <span>angles B are the same </span> </span>
And you can easily see that A + C + B does a complete rotation from one side of the straight line to the other, or <span>180°</span>
