In: Statistics and Probability
Each front tire of a vehicle is supposed to be filled to a
pressure of 25...
Each front tire of a vehicle is supposed to be filled to a
pressure of 25 psi (pounds per square inch). Suppose that X and Y
are random variables giving the actual air pressure on the right
and left tires, respectively. Suppose the joint pdf is given by
f(x,y)=K(x^2+y^2) for x and y between 20 and 30.
- Calculate the value K must have for this to be a pdf.
- Calculate the probability that both tires are
underfilled with air.
- Determine the marginal distribution of air pressure in the
right tire alone.
- Calculate the probability that the left tire's pressure is at
least eight more psi than the right tire's pressure.