For a continuous random variable x, the probability density function f(x) represents

a. the probability at a given value of x

b. the area under the curve at x

c. Both the probability at a given value of x and the area under the curve at x are correct answers.

d. the height of the function at x

Using probability concepts, it is found that the correct option is:

a. the probability at a given value of x

In a distribution, the notation f(x) is the equivalent to the probability of event x, that is:

Thus the correct option is a.

The area under the curve is given by the cumulative distribution, which is given by:

Thus it is not f(x).

And f(x) can also be the height of the relative frequency function, but not of the function itself.

A similar problem is given at link

Option d.

Step-by-step explanation:

we know that

The graph of a continuous probability distribution is a curve. Probability is represented by area under the curve.

The curve is called the probability density function (abbreviated as pdf).

We use the symbol f(x) to represent the curve

therefore

The probability density function f(x) represents . the height of the function at  x.

-13

step-by-step explanation:

f(x)=2x-5 for f(-4)

f(-4)   means let x=-4

f(-4) = 2(-4) -5

f(-4) =-8-5

      = -13

$25

step-by-step explanation:

25 - 4.50 = 20.5

20.5 / 2 = 10.25

10.25 + 10 = 20.25

20.25 - 12.50 = 7.75

therefore the answer is $25 as shown as the first number.