A discrete random variable $X$ taking non-negative values has the following moment generating function $M_X(t) = e^{2(e^t-1)},; -\infty < t < \infty$ Then, the value of $P(X \le 1)$ is:
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Let $X$ be a continuous random variable such that $E|X| < \infty$ and
$P\left(X \ge \frac12 + x\right) = P\left(X \le …
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Which of the following statements is not true?
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Let $X$ be a random variable having distribution function $F(x)$. Then which of the following statements may not be tru…
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A discrete random variable follows Poisson distribution with parameter $3$. The value of $E(X-6)^2$ is:
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Number of arbitrary constants in the equation of a cone is:
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The following system of equations:$2x_1 + x_2 - x_3 = 2$$3x_1 + 2x_2 + x_3 = 3$has:
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Condition that the plane $lx + my + nz = p$ should touch the ellipsoid
$\frac{x^2}{a^2} + \frac{y^2}{b^2} + \frac{z^2}{…
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In simple random sampling without replacement, the probability that a specified unit of the population will be included…
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The equation $yz + zx + xy = 0$ represents:
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Simpson’s one-third rule for evaluation of $\int_a^b f(x),dx$ requires the interval $[a,b]$ to be divided into:
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Max $z = 6x_1 - x_2$Subject to$2x_1 - x_2 \le 2$$x_1 \le 3$$x_1, x_2 \ge 0$The above LPP has:
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The Laplace transform of $\sin \sqrt{x}$ is:
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The solution of the differential equation
$y\sin 2x,dx - (y^2 + \cos^2 x),dy = 0$ is:
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The solution of
$3\frac{\partial^2 z}{\partial x,\partial y} - 2\frac{\partial^2 z}{\partial y^2} - \frac{\partial z}{\…
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The sampling scheme in which only first unit is selected randomly is known as:
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An integrating factor of
$\frac{dy}{dx} = \frac{1}{3x + y^2 + 2}$ is:
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Let $T:\mathbb{R}^4 \rightarrow \mathbb{R}^3$ be a linear transformation defined by
$T(x_1,x_2,x_3,x_4)=C(x_1-x_2,;x_2…
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Which of the following is a 2-dimensional subspace of $\mathbb{R}^3$?
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Let $X_1, X_2, … , X_n$ be i.i.d. random variables having pdf
$f(x) = (1/θ) e^{-x/θ},; 0 < x < ∞,; θ > 0$
The cdf of …
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$ \lim_{x→0} (cosec x)^{1/log x} $
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