a) Find asymptotes of the graph of the function
To find the asymptotes of the graph of the given rational function, we need to consider the horizontal asymptote(s) and vertical asymptote(s).
Horizontal Asymptote(s):
The horizontal asymptote(s) of a rational function are determined by the degree of the numerator and the denominator polynomials.
If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is y = 0.
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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) Verify Euler’s theorem for the function
a) Integrate
c) A club has 9 member having ages 21, 28, 23, 29, 52, 43, 32, 37 and 30 years. One has to be at least 30 years of age to be eligible for the presidentship of the club. A simple random sample of size 5 is selected to provide an estimate of the population proportion eligible for presidentship. Find the mean and the standard error of this estimate
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.
c) A garden pea plant is genetically mixed for the gene pair Tt, where the gene T (for tall) is dominant over the gene t (for short). The plant produced 40 tall and 20 short offspring. Using test find out whether the plant was self fertilized or fertilized by a short plant at 5% level of significance.
State whether the following statements are true or false giving reasons in support of your answer.
i) A binomial distribution has mean 3 and variance 4.
ii) The function has no maxima or minima.
iii) The line of regression of x on y is the same as the line of regression of y on x .
iv) The plane is parallel to the line
v) A continuous random variable can have probability density function