Question

Each rear tire on an experimental airplane issupposed to be filled with a pressure of 40 pound per squareinch(psi).Let X denote the actual air pressure for the right tireand Y denote the actual air pressure for the left tire.Suppose that Xand Y are random varibles with the jointdensity

f(x,y)= k(x²+², 30<-x<50;
30<-y<50
0, elsewhere
find k

Answer 1

The value of k in the joint pdf can be determined by setting up and solving a double integral over the range of x and y, making sure that the total probability equals 1.

Step-by-step explanation:

The student was asked to find the value of k in the joint probability density function (pdf) of two random variables, X and Y, which represent the air pressure in the right and left tires of an experimental airplane, respectively. The given pdf is f(x,y) = k(x² + y²) with a specified range for x and y: 30 < x < 50 and 30 < y < 50.

To determine the value of k, we must integrate the joint pdf over the respective ranges of x and y, and set the result equal to 1, which represents the total probability for all possible outcomes. We set up a double integral:

∫ ∫ f(x,y) dx dy = 1

Plugging in our function, we get:

∫3050 ∫3050 k(x² + y²) dy dx = 1

Performing the integration over y first and then x, we would find the exact value for k.

The absolute pressure concept from physics plays a role in understanding the context of tire pressure as it is related to gauge pressure and atmospheric pressure.