Math Answers

A grocery shop sell milk packets containing half a litre of milk. It makes bulk purchase of the same from the nearby city. Every time a purchase is made, it incurs a cost of Rs.50 towards transportation. The daily demand of packets is about 250. The holding cost is Rs. 0.10 for a packet per day to preserve it in a refrigerator. Determine the optimum quantity of a bulk purchase and the cycle time.

A bank wishing to determine the average amount of time a customer must wait to be
served took a random sample of 100 customers and found that the mean waiting time
was 7.2 minutes. Assuming that the population standard deviation is known to be
15 minutes, find the 90% confidence interval estimate of the mean waiting time for
all the bank’s customers.

1) Which of the following statements are true and which are false? Justify your answer with a
short proof or a counterexample.
i) The relation ∼ defined by R by x ∼ y if x ≥ y is an equivalence relation.
ii) If S1 and S2 are finite non-empty subsets of a vector space V such that [S1] = [S2], then
S1 and S2 have the same number of elements.
iii) For any square matrix A, ρ(A) = det(A)
iv) The determinant of any unitary matrix is 1.
v) If the characteristic polynomials of two matrices are equal, their minimal polynomials are
also equal.
vi) If the determinant of a matrix is 0, the matrix is not diagonalisable.
vii) Any set of mutually orthogonal vectors is linearly independent.
viii) Any two real quadratic forms of the same rank are equivalent over R.
ix) There is no system of linear equations over R that has exactly two solutions.
x) If a square matrix A satisfies the equation A2 = A, then 0 and 1 are the eigenvalues of
A.

For the random variable X with the following probability density function
f (x) ={2e^(-2x); 0 is greater than equal to x and 0; 0 is smaller than x
find
i) ) P (| X − μ | >1
ii) Use Chebyshev’s inequality to obtain an upper bound on P[| X − μ | >1] and
compare with the result in (i).

Which of the following statements are true or false? Give reasons for your answers. iv) If correlation coefficient between x and y is 0.62., then correlation coefficient between u and v will by 0.62, where U=5+6xand V =7-3y

Which of the following statements are true or false? Give reasons for your answers. By Chebyschev’s inequality, P{mode of x- my greater than equal to 2 sigma} smaller than equal to 0.2

Which of the following statements are true or false? Give reasons for your answers. i) If X has the distribution N(9,10)and if Y=5x-3, then Y has distribution N(84,53)

true or false? Give reason
If correlation coefficient between x and y is 0.62 , then correlation coefficient
between u and v will be 0.62 , where u = 5 + 6x and v = 7 − 3y .