Solve: 2x + 3y = 4 and 4x + 6y = 8 using Cramer's rule.

If f'(x) = 8x³ -2x², f(2) = 1, find f(x)

If the marginal revenue for a commodity is MR = 9 - 6x² + 2x, find the total revenue function.

Form the differential equation of family of rectangular hyperbolas whose asymptotes are the Co-ordinate axes.

If f(0) = 5, f(1) = 6, f(3) = 50, find f(2) by using Lagrange's formula.

An unbiased die is rolled. If the random variable X is defined as
X(w) = {1, the outcome w is an even number    
{0, if the outcome w is an odd number
Find the probability distribution of X.

A continuous random variable. X has the p.d.f. defined by \(f(x)=\left\{\begin{array}{l} C e^{-a x}, \quad 0<x<\infty \\ 0, \quad \text { elsewhere } \end{array}\right.\) Find the value of C if a> 0

If 10 coins are tossed, find the probability that exactly 5 heads appears.

A sample of 400 students is found to have mean height of 171.38 cms, Can it reasonable be regarded as a sample from a large population with mean height of 171.17 cms and standard deviation of 3.3 cms (Test at 5% level)

The following is the pay-off matrix (in rupees) for three strategies and three states of nature. Select a strategy using maximin principle.