HW 4 

[PG] Pages 158-159: Exercises:  15, 16, 19

[PG] Pages 191-192: Exercises: 1, 2, 8, 9

Chapter 6 (pages 158-159)
15. a.  sensitivity = P(+rv|cad)=302/481 = 0.628
        specificity = P(-rv|cad)=372/452 = 0.823
    b. Since P(cad)=0.10, P(no cad)=0.10, the predictive value of   
the positive test is
    
P(cad|+rv) = P(+rv|cad)P(cad)/[P(+rv|cad)P(cad)+P(+rv|no cad)P(no cad)]
           = (0.628)(0.10)/[(0.628)(0.10)+(0.177)(0.90)] = 0.283.
    c. The predictive value of a negative test is
         P(no cad|-rv)=0.592

16. a. As the cutoff point is raised, the specificity increases and the 
probability of a false positive result decreases. Furthermore, the       
sensitivity decreases and the probability of a false negative result
increases.

b. 
c. In this case, the sensitivity and specificity will both be high no
matter which cutoff value we select. A level of 9 ng/ml is probably best
for maximizing sensitivity and specificity simultaneously; this point 
lies closet to the upper left corner of the graph. 

Chapter 7 (1, 2, 8, 9)

1. A probability distribution is a funtion that describes behavior of
a random variable. In the discrete case, it specifies all possible 
outcomes of the random variable along with the probability that 
each will occur. In the continuous case, it specifies the probabilities
associated with specific ranges of values. 

2. Parameters are numerical quantities that summarize the characteristics
  of a probability distribution. Examples of parameters include the (n, p)
  in the binomial distribution, and the ``lambda'' in the Poisson 
  distribution. 

8, a.
   b. 0.031
   c. P(X => 1) = 0.329
      P(X => 4)=0.016
   d. P(X=3|X =>1) = 0.094

9. It is unlikely that X has a binomial distribution.