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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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
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 |
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?
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.
Distinguish between ‘Age Replacement’ and ‘Block Replacement’ policies
Let the lifetimes Y1 ,Y2 ,...., are independently and identically distributed random variables and follows negative exponential distribution with parameter 5. If lifetimes T > 0 and age replacement policy is to be employed, then:
i) find the mean renewal time and
ii) find the long-run average cost per unit time, given the costs C1 4 = and C2 = 6units
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.