A dealers profit in units of 5,000 on a new auto there is a random variable X having density function

a) find the variance in the dealers profit

b) Demonstrate that chebyshevs inequality holds for k=2 with the density function above

c) what is the probobility that the profit exceeds $500

For part a i got

which i know is correct.

which i know is correct.

Therefore,

for part b chebyshevs inequality

Chebyshev's inequality is usually written as

What we know:

adding them into the chebyshevs we have

I dont know what to do from here. Would i move the 1/3 to the right side of the inequality?

then use that as a limit in an integral?

for part c

therefore use lower limit 1/10 and upper limit 1 in an integral?