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Recent questions tagged p243

If a random variable $X$ follows poisson distribution such that $E(X^{2})=30$ then the variance of the distribution is

asked May 30, 2013 by poojasapani_1

1 answer

If in a poisson distribution $P(X=0)=k$ then the variance is

asked May 30, 2013 by poojasapani_1

1 answer

If $2$ cards are drawn from a well shuffled pack of $52$ cards, the probability that they are of the same colours without replacement, is

asked May 30, 2013 by poojasapani_1

1 answer

A box contains $6$ red and $4$ white balls.If $3$ balls are drawn at random, the probability of getting $2$ white balls without replacement, is

asked May 28, 2013 by poojasapani_1

1 answer

In $16$ throws of a die getting an even number is considered a success. Then the variance of the successes is

asked May 28, 2013 by poojasapani_1

1 answer

If the mean and standard deviation of a binomial distribution are $12$ and $2$ respectively. Then the value of its parameter $p$ is

asked May 28, 2013 by poojasapani_1

1 answer

The mean of a binomial distribution is $5$ and its standard deviation is $2.$ Then the value of $n$ and $p$ are

asked May 28, 2013 by poojasapani_1

1 answer

In $5$ throws of a die, getting $1$ or $2$ is a success. The mean number of successes is

asked May 28, 2013 by poojasapani_1

1 answer

Var $(4X+3)$ is

asked May 28, 2013 by poojasapani_1

1 answer

$\mu_{2}=20, \mu'_{2}=276$ for a discrete random variable $X$. Then the mean of the random variable $X$ is

asked May 28, 2013 by poojasapani_1

1 answer

Choose the correct answer in the slope of the tangent to the curve \(x = t^2 + 3t – 8, y = 2t^2 – 2t – 5\) at the point \((2,– 1)\) is

asked Nov 28, 2012 by thanvigandhi_1

1 answer

Choose the correct answer in a cylindrical tank of radius 10 m is being filled with wheat at the rate of 314 cubic metre per hour. Then the depth of the wheat is increasing at the rate of

asked Nov 28, 2012 by thanvigandhi_1

1 answer

Show that height of the cylinder of greatest volume which can be inscribed in a right circular cone of height \(h\) and semi vertical angle $\alpha$ is one-third that of the cone and the greatest volume of cylinder is $\large \frac{4}{27}$$\pi h^3 \: tan^2 \: \alpha $

asked Nov 28, 2012 by thanvigandhi_1

1 answer

Show that the height of the cylinder of maximum volume that can be inscribed in a sphere of radius R is \(\large\frac{2R}{\sqrt 3}\) . Also find the maximum volume.

asked Nov 28, 2012 by thanvigandhi_1

2 answers

Let \(f\) be a function defined on \([a, b]\) such that \(f' (x) > 0\), for all \(x \: \in (a, b)\). Then prove that \(f\) is an increasing function on \((a, b).\)

asked Nov 28, 2012 by thanvigandhi_1

1 answer

Show that the altitude of the right circular cone of maximum volume that can be inscribed in a sphere of radius \(r\) is \( \large\frac{4r}{3}\)

asked Nov 28, 2012 by thanvigandhi_1

1 answer

Find the absolute maximum and minimum values of the function $(f)$ given by $ f (x) = cos^2 x + sin\: x, x\: \in [0, \pi]$

asked Nov 28, 2012 by thanvigandhi_1

1 answer

Find the points at which the function \(f\) given by \(f (x) = (x – 2)^4 (x + 1)^3\) has a (i) local maxima, (ii) local minima and the (iii) point of inflexion.

asked Nov 28, 2012 by thanvigandhi_1

1 answer

A point on the hypotenuse of a triangle is at distance \(a\) and \(b\) from the sides of the triangle.Show that the maximum length of the hypotenuse is $ (a^{\large\frac{2}{3}} + $$b^{\large\frac{2}{3}})^{\Large\frac{3}{2}}$

asked Nov 28, 2012 by thanvigandhi_1

1 answer

A window is in the form of a rectangle surmounted by a semicircular opening. The total perimeter of the window is 10 m. Find the dimensions of the window to admit maximum light through the whole opening.

asked Nov 28, 2012 by thanvigandhi_1

1 answer

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