b) Verify Euler’s theorem for the function
a) Find the radius of the sphere which passes through the points ),1,0,0( ),,0,0,1( )0,1,0( and ).1,0
See Answer →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
See Answer →b) Find the mean and the standard deviation of a random variable with the following probability density function:
a) Integrate
c) In a certain Poisson distribution the probability of 3 successes is exactly equal to the probability of 4 successes. Find its mean and standard deviation. Also find the probability of more than 1 success for the given distribution.
See Answer →b) Find the term independent of a in the binomial expansion of
a) Find asymptotes of the graph of the function
Eliminating z from and
gives
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 |
See Answer →
b) A bag contains 3 white balls and 2 red balls. Another bag contains 5 white and 3 red balls. A bag is chosen at random and a ball is drawn from it. Find the probability that it is white.
See Answer →a) Define Is f injective, surjective, monotone?
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
Evaluate
Find the points of inflexion of the curve Also, show that they lie on a straight line.
Find the slope of the normal to the curve
Evaluate
Find the least value of where
If the first three non-zero terms of Maclaurin’s series for sin x are used to approximate sinπ ,2/ show that the error is less than 1/50.
See Answer →Find the perimeter of the cardioid