Assigned Mar 12
Due Mar 17th Beginning of Class
Question 1
Estimate the integral of sin(x2) from 2 to 3. Note, this function is not always
greater than 0 in this range.
Question 2
At the Tunbridge World's Fair, a coin toss game works as follows. Quarters
are tossed onto a checkerboard. The management keeps all the quarters, but
for each quarter landing entirely within one square of the checkerboard the
management pays a dollar. Assume that the edge of each square is twice the
diameter of a quarter, and that the outcomes are described by coordinates
chosen at random. Is this a fair game?
Question 3
Assume that a new light bulb will burn out after t hours, where t is chosen
from [0, infinity) with an exponential density
f (t) = lambda * e-lambda * t .
In this context, lambda is often called the failure rate of the bulb.
- Assume that lambda = 0.01, and find the probability that the bulb will not
burn out before T hours. This probability is often called the reliability
of the bulb.
- For what T is the reliability of the bulb = 1/2?