A basket contains 4 puppies: one of the puppies has 1 spot, one of the puppies...

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A basket contains 4 puppies: one of the puppies has 1 spot, one of the puppies has 2 spots, and the remaining two puppies have 4 spots. Suppose two puppies are selected at random without replacement. Let the random variable X equal the total number of spots on the selected puppies. (a) Find the probability distribution of X. (b) Find the probability that the puppies have a total of 5 spots, i.e. find P(X 5). (c) Find the probability that the puppies have a total of 6 or more spots, i.e. find P(X 2 6). (d) Find the probability that the puppies have 5 or fewer spots or 8 spots, i.e. find P(X <5 or X = 8). (e) Given that the puppies have 6 or more spots, determine the probability that both puppies have 4 spots each (i.e. 8 spots total), i.e. find P(X = 8|X 2 6). (f) On average, how many spots do we expect on the two selected puppies? (g) Compute o? = Var(X). %3D A basket contains 4 puppies: one of the puppies has 1 spot, one of the puppies has 2 spots, and the remaining two puppies have 4 spots. Suppose two puppies are selected at random without replacement. Let the random variable X equal the total number of spots on the selected puppies. (a) Find the probability distribution of X. (b) Find the probability that the puppies have a total of 5 spots, i.e. find P(X 5). (c) Find the probability that the puppies have a total of 6 or more spots, i.e. find P(X 2 6). (d) Find the probability that the puppies have 5 or fewer spots or 8 spots, i.e. find P(X <5 or X = 8). (e) Given that the puppies have 6 or more spots, determine the probability that both puppies have 4 spots each (i.e. 8 spots total), i.e. find P(X = 8|X 2 6). (f) On average, how many spots do we expect on the two selected puppies? (g) Compute o? = Var(X). %3D

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a Out of 4 puppy one puppy has one spot two puppies has 4 spots a... View the full answer