There are 10% defective pens. In a sample of randomly selected 10 pens, the probability that atmost one pen is defective, is

The probability distribution of a random variable X is given as:

$P(X=x) = \begin{cases} kx^2 & for & x=1,2,3 \\ 2kx & for & x=4,5,6 \\ 0 & otherwise \end{cases}$

Where $k$ is an arbitrary constant, then $E(X)$ is equal to:

If X has a Poisson distribution such that $P(X = 1) = P(X = 2)$ then $P(X = 3)$ is :

In a random experiment, a collection of trials is called Bernoulli trials if

A. The number of trials is infinite.

B. The trials are independent of each other.

C. Each trial has exactly two outcomes, defined as success and failure.

D. The probability of success will vary in each trial.

Choose the correct answer from the options given below:

In a binomial distribution, the sum of its mean and variance is 1.8. If the event was conducted 5 times, then the probability of 3 successes is

In binomial distribution with $n = 10$ and $P = \frac{1}{3}$, the probability of the event that unequal number of failures and successes occur is :

If the random variable X follows the Poisson distribution such that P[X = k] = P[X = k+1], then the mean value of X is: