Engineering Mat...

A student tries to breaks his pencil of unit length two pieces uniformly. The expected length of the shorter piece of pencil is _____.

X is a continuous random variable with probability density function given by

f(x) = kx                (0 ≤ x < 2)

       = 2k               (2 ≤ x < 4)

       = -kx + 6k      (4 ≤ x < 6)

Let X be a Discrete random variable following binominal probability distribution \({\left( {q + p} \right)^n} = {\left( {\frac{1}{3} + \frac{2}{3}} \right)^{10}}\).

The sum of the standard deviation and the variance of the above distribution is ________.

A coin is tossed 10 times. The probability of occurrence of 6^th tail in 10^th throw is

A random variable X had Poisson distribution. If 2P(X = 2) = P(X = 1) + 2P (X = 0) then the variance of X is

The probability density function of normal distribution of a random variable X is

\(f\left( x \right)\; = \;K{e^{\left( { - \frac{{{x^2}}}{{50}} + 4x - 200} \right)}}\;,\; - \infty \; < \;x\; < \; + \infty \)

What is the sum of mean and standard deviation?

100 students appear in a Testbook test and every student solved 80 Questions, each having 4 choices. Every correct answer gives +1 marks and every incorrect answer deducts -0.25 marks.

The expected marks of all the students appeared assuming that every answer from each student has been given randomly is ____