A community has two police cars, which operate independently of one another. The probability that a specific car will be available when needed is 0.99.
i) What is the probability that neither car is available when needed?
ii) What is the probability that a car is available when needed?
i) The probability that a specific car is not available when needed is \(1 - 0.99 = 0.01\). Since the two cars operate independently, the probability that _____ _______ _______ ___ ________ ______ __________ ________ ______ _______ ___ ____.
_______ __________ _____ _____ _________ ___ ________ ____ __________ _______ _____ ________.
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__________ __________ _________ _______ _______ _________ ________ _____ ________ ___ ____ ___.
__________ ___ _________ _______ _______ __________ __________.
_______ ________ ______ _______ ____ _____ __________ __________.
_________ ____ _______ ________ ________.
______ ________ _____ ________ ____ _____ _______ ___.
__________ _____ _________ ______ ______ ______ ________ ___ _______ ________ ________ _______.
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A study about a population showed that the mobility of population of a state to a village, town and city is in the following percentages:
| From | To | ||
| Village | Town | City | |
| Village | 60 | 25 | 15 |
| Town | 10 | 70 | 20 |
| City | 10 | 30 | 60 |
State whether the following statements are true or false. Justify your answer with a short proof or a counter example:
i) Although in one-step transition probability matrix, ,P of a Markov chain the sum of each row must necessarily be unity but in higher order transition probability matrices, . This rule is not necessary.
ii) For the joint pdf of random variables (X,Y) given by:
iii) Let the r.v. X follows the negative exponential distribution with parameterThen
iv) One of the examples of non-Poisson queuing system is the (M / G (:)1/ ∞ (FIF0) queuing model.
v) be a random sample from
then maximum likelihood estimators o
Let {Xn; }0 n ≥ be a Markov chain with four states; 1, 2, 3, 4 and the following transition probability matrix:
| 1 | 2 | 3 | 4 | |
| 1 | 0 | 0 | 1 | 0 |
| 2 | 1 | 0 | 0 | 0 |
| 3 | 1/2 | 1/2 | 0 | 0 |
| 4 | 1/3 | 1/3 | 1/3 | 0 |
State whether the following statements are true or false. Justify your answer with a short proof or a counter example:
i) Although in one-step transition probability matrix, P, of a Markov chain the sum of each row must necessarily be unity but in higher order transition probability matrices, P(j); j = 2,3,4,...... This rule is not necessary.
ii) For the joint pdf of random variables (X,Y) given by:
iii) Let the r.v. X follows the negative exponential distribution with parameter . Then
iv) One of the examples of non-Poisson queuing system is the (M/G/1): (∞(F1F0) queuing model.
v) If X1,X2,..., X, be a random sample from Np, (μ, Σ), then maximum likelihood estimators of µ and ∑are:
In a certain state, 58 landfills are classified according to their concentration of three hazardous chemicals: arsenic, barium and mercury. Suppose that the concentration of each one of the three chemicals is characterized as either high or low. If a landfill is chosen at random from among 58 landfills, given the following configuration:
|
| Barium | |||
| High Mercury | Low Mercury | |||
| Arsenic | High | Low | High | Low |
| High | 1 | 3 | 5 | 9 |
| Low | 4 | 8 | 10 | 18 |
The certain item is manufactured by three factories, say 1, 2 and 3. It is known that 1 turns out twice as many items as 2 and that 2 and 3 turn out the same number of items (during a specified production period). It is also known that 2 percent of the items produced by 1 and 2 are defective while 4 percent of those manufactured by 3 are defective. All the items produced are put into one stock pile and then one item is chosen at random. The chosen item was found defective. What is the probability that it was produced in factory 1?
A community has two police cars, which operate independently of one another. The probability that a specific car will be available when needed is 0.99.
i) What is the probability that neither car is available when needed?
ii) What is the probability that a car is available when needed?