Question

1. After 48 hours of hosting an infected deer tick in the nymph stage, the probability that a canine host contracts Lyme disease is 0.2. Nine dog hosts are randomly examined. Let X = the number of infected dogs.
   1. What discrete probability distribution best describes the probability of selecting X infected dogs when examining nine? Name the distribution and write down the equation (with all parameters assigned).
   2. Find the probability that exactly two dogs are infected.
   3. Find the probability that less than two dogs are infected.
   4. Find the probability that at least four dogs are infecte (Hint: use the complement rule)
   5. Find the mean, variance, and standard deviation of the random variable, X in (a).
2. 6. What discrete probability distribution best describes the probability of finding the first infected dog on the Xth examination?  Name the distribution and write down the equation (with all parameters assigned).
   7. Find the probability that the first infected dog is the fifth dog to be examined.
   8. What discrete probability distribution best describes the probability of finding the kth infected dog on the Xth examination? Name the distribution and write down the equation (with all parameters assigned)
   9. Find the probability that the second infected dog is the fifth dog to be examined.

Answer 1

Sol: Given,

X=The number of infected dogs

n=Dogs randomly selected

p=0.2

q=1-(0.2)=0.8

(a) X should follow Binomial distribution

i.e X~Binomial(9, 0.2)

(b)

Since this is a multiple part question, only first four parts are answered.