A farmer has 200 metres of fencing with which he wishes to enclose a rectangular field. One side of the field can make use of a fence that already exists. What is the maximum area he can enclose?
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Write down the sample spaces for the following experiments:
i) A coin is tossed and at the same time a die is rolled.
ii) The order in which a mouse, a frog, and a rabbit arrive at a lake is observed.
For what values of m will the equation
x 2 − 2x (1 + 3m) + 7 (3 + 2m) = 0
have equal roots?
Find the values of x for which the function
f ( x) = x 2 − 2x + 1
is increasing or decreasing. Sketch the graph of y = f (x) .
A continuous random variable X has the p.d.f.
Calculate the mean and standard deviation of X . Construct the distribution function F ( x) and hence evaluate P( X > 1/4) .
Find the probability of drawing an ace or a spade from a deck of 52 cards in a single draw.
The following data were obtained in a study of the relationship between the resistance (ohms) and the failure time (minutes) of certain overloaded resistors.
| Resistance | 48 28 33 40 36 39 46 40 30 42 44 48 39 34 47 |
| Failure time | 45 25 39 45 36 35 36 45 34 39 51 41 38 32 45 |
An economist wants to estimate the relationship between a family’s annual income and the amount that the family saves. The family data for nine families are obtained
| Annual income (thousands of Rs.) | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
| Annual saving (thousands of Rs.) | 0.0 | 0.1 | 0.2 | 0.2 | 0.5 | 0.5 | 0.6 | 0.7 | 0.8 |