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b) Find the mean and the standard deviation of a random variable with the following probability density function:
a) Find (a × b)⋅ c where
a) A and B are two events which are independent. The probability that both A and B occur is and the probability that neither of them occurs is
Find the probability of the occurrences of A and B.
a) Define Is f injective, surjective, monotone?
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.
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.