The probabilities are 0.4, 0.2, 0.3 and 0.1, respectively, that a delegate to a certain convention arrived by air, bus, automobi
le, or train.
a. Consider 9 randomly selected delegates at this convention. What is the probability that from these 9 delegates, 3 arrived by air, 3 arrived by bus, 1 arrived by automobile, and 2 arrived by train?
b. Consider 9 randomly selected delegates at this convention. Suppose we are only interested in the delegates arriving by bus. What is the probability distribution of X: the number of delegates that arrived by bus?What is the probability that all 9 delegates arrived by bus?
c. Consider 9 randomly selected delegates at this convention. Suppose we are only interested in the delegates arriving by train. What is the probability distribution of X: the number of delegates that arrived by train? What is the expected value of the number of delegates that arrived by train?
d. Suppose now we are interested in delegates arriving by automobile. Suppose X represents the number of delegates that arrive until 5 have arrived by automobile. What is the distribution of X? What is the probability that exactly 10 delegates will arrive until 5 have arrived by automobile?
e. Suppose the delegates arrive at a rate of 3 delegates per hour. What is the probability that 5 delegates arrive over a two hour period?
a. Consider 9 randomly selected delegates at this convention. What is the probability that from these 9 delegates, 3 arrived by air, 3 arrived by bus, 1 arrived by automobile, and 2 arrived by train?
b. Consider 9 randomly selected delegates at this convention. Suppose we are only interested in the delegates arriving by bus. What is the probability distribution of X: the number of delegates that arrived by bus?What is the probability that all 9 delegates arrived by bus?
c. Consider 9 randomly selected delegates at this convention. Suppose we are only interested in the delegates arriving by train. What is the probability distribution of X: the number of delegates that arrived by train? What is the expected value of the number of delegates that arrived by train?
d. Suppose now we are interested in delegates arriving by automobile. Suppose X represents the number of delegates that arrive until 5 have arrived by automobile. What is the distribution of X? What is the probability that exactly 10 delegates will arrive until 5 have arrived by automobile?
e. Suppose the delegates arrive at a rate of 3 delegates per hour. What is the probability that 5 delegates arrive over a two hour period?
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