Aparabolic satellite dish reflects signals to the dish’s focal point. an antenna designer analyzed signals transmitted to a satellite dish and obtained the probability density function f(x) = c(1 - 1/16x^2) for 0 < x < 3, where x is the distance (in meters) from the centroid of the dish surface to a reflection point at which a signal arrives. determine the value of c that makes f(x) a valid probability density function

Step-by-step explanation:

The probability density function is :

With 0 < x < 3

To be a valid probability density function :

Where a < x < b

And also

f(x) ≥ 0 for a < x < b

Applying this to the probability density function of the exercise :

We can verify by replacing ''c'' in the original probability density function and integrating :

Also, f(x) ≥ 0 for 0 < x < 3

answer: 140

step-by-step explanation:

so just add all then it will be your answer but i am not pretty sur eif it is but hope this i am here to people

step-by-step explanation:

we have

using a graphing tool

see the attached figure

this is a quadratic equation (vertical parabola) open up

the vertex is a > vertex

the domain of the function is all real > interval (-∞,∞)

the range of the function is the > [-6.125,∞)

the function has two x->   and

the function is increasing over the > (0.25,∞)

the function is decreasing over the > (-∞,0.25)