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 unavailable. Since the cars operate independently, the probability of both cars being _____ _________ _________ _____ _______ _________ _____ ___.
_______ ____ ________ _____ ___ _______ _________ __________.
_____ _________ _____ ________ _______ _________ ____ ______ ___ ____.
_________ __________ _________ ______ _______ ___ ___ ________.
_______ _____ __________ ________ _______ ______ ___ _________ __________ _____ ________.
________ ____ ______ ____ ______ _________ ___ ________ ________ ____ ____.
______ ____ _________ ________ __________ _____ _________ ______ ___ ____ _________ _________.
_____ ________ __________ ________ _________ ____.
__________ _____ ________ _____ ______ _____ ____ ___ ____ ____.
_______ _____ ____ ______ ____ _________ ___ _____.
___ _______ ________ ____ _________ _____ _________ _______ __________ ________.
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In order to fit the regression line y = β1 + β2 on a data set consisting of 34 pairs of values (z,y), the least square estimates of β1 and β2 are to be computed. From the data set, the following values are obtained:
Obtain the fitted regression line.
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?
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 |
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 |
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?
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.
What is branching process? Give two real examples of branching process.
If )s(P and P )s( n respectively is the probability generating function (pgf ) of the i.i.d.
random variables and the random variables
Then show that:and