Answers for the Practice Second Test

Mathematics 3C

1.   (a)   0.18, or 18%.   Multinomial: 1 and 1 and 1.
(b)   Five flips.   Geometric, p = 0.2. E(W) = 1/p.
(c)   16/125, or 0.128.   Geometric, p = 0.2.

2.   41/e^8.   Poisson, lambda = 2 and Lambda = 8. P(S is 0 or 1 or 2).

3.   (a)   1/2.   First get the density function by differentiating the cumulative distribution.
(b)   1/20.   First calculate E(X^2), which is 3/10.

4.   (a)   1/e^2.   Exponential with lambda = 2 per day.
(b)   1/e^{17/8}.  
(c)   It is 1/2 or less.  

5.   0.0796.   Normal approximation to the binomial distribution. Be sure to use the histogram correction.

6.   0.098.   The pill problem.