Seasonal variations are __________

The normal equations for estimating a and b so that the line y = ax + b may be the line of best fit are __________

The point estimate variance of 21, 25, 20, 16, 12, 10, 17, 18, 13 and 11 is _______

The standard error of the sample mean is __________

For a standard normal distribution, the mean and variance are _________

In a binomial distribution, n = 4, p(X = 0) = \(\frac{16}{81}\), then p(X = 4) is ___________

In a binomial distribution if the mean is 8 and the variance is 6, then the number of trials is ___________

Which of the following are correct?
(i) E(aX+b) = a E(X) + b
(ii) μ₂= μ₂¹ - (μ₁¹)²
(iii) μ²= variance
(iv) V (a X + b) = a² V(x)

If F(x) is the probability distribution function, then F(- ∞) is_______.

If F(x) is the probability distribution function, then F(- ∞) is_______.

Given E(X + c) = 8 and E(X - c) = 12, then the value of c is ___________

The penalty is the difference between the ___ costs in each row and column.

The optimum_______schedule remains, unaltered if we add or subtract a constant from all the elements of the row or which of the cost________matrix.

The equation of ydx + xdy = e^-xy dx if it cuts the Y-axis is ______

The solution of \(\frac { d^{ 2 }y }{ dx^{ 2 } } \) - y = 0 is _____________

The solution of \(\frac { dy }{ dx } \) = e^x-y is _____________

The differential equation satisfied by all the straight lines in xy plane is _____________

\(\int _{ 1 }^{ 4 }{ f\left( x \right) } dx,\) where f(x) =  \(\begin{cases} 7x+3\quad if\quad 1\le x\le 3 \\ 8x\quad if\quad 3\le x\le 4 \end{cases}\) is _____________.

\(\int { \frac { 1 }{ 1+sinx } } \) dx = ____________ +c

∫ e^{3 log x} (x⁴ +1)^-1 dx = ____________ +c

If \(\int { \frac { 1 }{ \left( x+2 \right) \left( { x }^{ 2 }+1 \right) } } \) dx = a log \(\left| 1+{ x }^{ 2 } \right| \) +b tan^-1 x + \(\frac { 1 }{ 5 } log\left| x+2 \right| \) +c then ___________

If \(\left| \begin{matrix} 2x & 5 \\ 8 & x \end{matrix} \right| =\left| \begin{matrix} 6 & -2 \\ 7 & 3 \end{matrix} \right| \) then x =

In Newtons forward and backward interpolation formula, the first two terms will give the __________ interpolation

 The nationality of the mathematician Joseph Louis Laguange is _________

Δ[f{x) . g(x)] = __________

The area below the demand curve p = f(x) and above the line p = p_o is________.

The Consumer's surplus for the demand function P =f(x) for the quantity X_o and price P_o is_________

The area of the region bounded by the line y = 3x + 2, the X-axis and the ordinates x = - 1 and x = 1is_________ sq. units.