In a random experiment, a collection of trials is called Bernoulli trials then which of the following statements are TRUE?

A. The number of trials is infinite.

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

C. The trials are dependent by nature.

D. The probability of success remains the same in each trial.

Choose the correct answer from the options given below:

Between 3 p.m. and 5 p.m. the average number of phone calls per minute coming into the helpline desk of a bank is 5. The probability that during one particular minute there will be only one phone call is :

On a multiple choice examination with four possible answers (out of which only one is correct) for each of five questions, what is the probability that a candidate would get four or more correct answers just by guessing?

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 the probability distribution of a random variable X is given as

Then the mean of X is

A discrete random variable X has the following probability distribution :

The value of b is :