b) Obtain
To evaluate the integral:
\[ \int \tan^{-1}\left(\frac{2x}{1-x^2}\right) \, dx \]
we can use the substitution method.
Let \( u = \frac{2x}{1-x^2} \).
Then,
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c) Compute the correlation co-efficient between X and Y for the following data:
| x | 9 | 7 | 6 | 1 | 3 | 9 | 4 |
| y | 1 | 3 | 5 | 6 | 9 | 6 | 4 |
c) The difference of mean and variance of a binomial distribution of 9 trails is 4. Find the probability p of success of the binomial distribution. Also find the probability of (i) exactly two successes and (ii) less than 2 successes.
b) Show that sin x 1( + cos x) has a maximum at
b) Find two positive numbers x and y such tha 60and
is maximum.
a) It is known that 10 men out of every 100 men and 30 women out of every 1000 women are color blind. In a community, half the population is male. Using Baye’s theorem find the probability that a color blind person chosen at random from among all color blind persons in the community is male.
c) Two groups of 10 plants each were grown on two different fertilizers. The average height of first group of plants was 92.44 cm, with a standard deviation of 4 cm. For the second group, the average height was 90 cm with a standard deviation of 2 cm. At 5% level of significance test the hypothesis that first fertilizer is better than the second in terms of the plant growth.
a) Integrate