The probability that a student passes a Physics test is
and the probability that the student passes both a Physics test and an English test is The probability that the
student passes at least one test is What is the probability that the student passes the English test?
We are given the following probabilities: - The probability that the student passes the Physics test, \( P(\text{Physics}) = \frac{2}{3} \) - The probability that the student passes both the Physics and English tests, \( P(\text{Physics} \cap \text{English}) ________ _____ _____ ______ ___ ________ ______ ________ _______ ______ _______.
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The joint probability distribution of x and y is given below:
| 0 | 1 | 2 | ||
| 0 | ||||
| 1 | ||||
| 2 | __ | |||
| 3 | __ | |||
Find (i) )
(ii) )
(iii) )
(iv) )
The police plans to enforce speed limits by using radar traps of 4 different locations within the city. The radar traps at each of the locations and
are operated 40 % 30% 20% and 30%, of time. If a person who is speeding on h, is way to work has probabilities of 0.2, 0.1, 0.5 and 0.2 respectively of passing through these locations. What is the probability that the person will receive a speeding challan.
a) Find the mean and standard deviation for the following data:
| Class interval | Frequency |
| 0 – 10 | 5 |
| 10 – 20 | 10 |
| 20 – 30 | 14 |
| 30 – 40 | 15 |
| 40 – 50 | 6 |
b) State Chebychev’s inequality. Hence obtain the lower bound for if the E(x) and
of x are 4 and 20 respectively.
Show that variance can be expressed in terms of the mutual differences of the observations i.e.
Let p be the probability that a coin will fall head in a single toss in order to test against
The coin is tossed 3 times and
is rejected if more than 2 heads are obtained. Find the probability of type I and type II errors. Also obtain the power of the test.
If Find the moment generating function of x − c where c is constant.
Every clinical thermometer is classified into one of the four catergories A, B, C and D on the basis of inspection and test. From the past experience it is known that thermometers produced by a certain manufacturer are distributed among the four categories in the following proportions:
| Category: | A | B | C | D |
| Proportion: | 0.87 | 0.009 | 0.003 | 0.01 |
| Category: | A | B | C | D |
| No. of thermometers Reported: | 1188 | 91 | 47 | 10 |