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) To find the probability that neither car is available when needed, we need to calculate the probability that both cars are _____ ________ _____ _______ ___ ___ ______ _________.
___ _________ _________ ___ _______ ____ ________.
___ ___ _________ __________ ___ ______ __________ _______ __________ ______.
____ ______ ______ _______ ____ _______ ___ __________ _________ _______ _____ _____.
_______ __________ _____ ______ ________.
________ ________ _____ ___ _________ ________ _________ ________.
____ ______ ________ ___ _____ _____ ___ _________ ________.
_____ _______ ____ ________ _________ ___.
_______ ________ ________ _________ _________ __________ _______.
_______ ______ _______ _________ _________ _______ ____ _________ ___.
__________ _____ ___ __________ ___ _________ ___ _______ ________ __________ ___.
_________ __________ _______ _________ ___ _________ ______ ____ __________ ______ ______.
__________ ______ _________ _________ ____ _______ ___ ______.
______ ___ ______.
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The joint distribution of the random variables X and Y is given by:
| y/x | -1 | 0 | 1 |
| -1 | α | β | α |
| 0 | β | α | β |
| 1 | α | β | α |
What is the purpose of principal component analysis? Given the covariance matrix of order 2× ,2 explain how would you extract the principal components. Also, explain how would you find the proportion of total population variance for all the principal components.
It is claimed that the function is the joint 16
distribution function of the random variables X and Y. Then:
i) determine the corresponding joint probability density function fx,y and
ii) calculate the probability
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 |
What is the purpose of principal component analysis? Given the covariance matrix of order 2× ,2 explain how would you extract the principal components. Also, explain how would you find the proportion of total population variance for all the principal components.
Consider the following system considering of two switches I and II between two points A and B:
A signal is sent from the point A to point B and is received at B if both the switches I and II are closed. It is assumed that the probabilities of I and II being closed are 0.8 and 0.6 respectively and that P [II is closed] I is closed] = P [II is closed].
Find:
i) The probability that signal is received at B.
ii) The conditional probability that switch I was open, given that the signal was not received at B,
iii) The conditional probability that switch II was open, given that the signal was not received at B.
What is branching process? Give two real examples of branching process.
If P(s) and Pn(s) respectively is the probability generating function (pgf) of the i.i.d. random variables and the random variables {Xn}, where Xn+1 =
Then show that:
Pn(s) = Pn-1(P(s))
and Pn(s) = Pn-1(P(s)).