A dealer's profit in units of $5,000 on a new automobile is a random variable X having density function
f(x,y) = 2(1-x) for -1 <= x <= 1
a) Find the vaiance in the dealer's profit.
b) Demonstrate that chebyshev's inequality holds for k = 2 with the density function above.
c) What is the probability that the profit exceeds $500?
a) E(2(1-x)) = -4
What is f(x) in this problem?
b) How can I show that it holds true?
c) ???
b) Chebyshev's Inequality: .
So you first need to calculate:
1. .
2. ,
where (which will answer part a) by the way).
Therefore .
Substitute , and k = 2 into the left hand side of Chebyshev's Inequality:
which demonstrates the inequality.
Most of this is basic application of routine definitions and formulae.
NB: I reserve the right for the arithmetic details to contain errors so make sure you carefully check all numerical results given above.