The random variable X has a probability distribution $P(X)$ of the following form, where $k$ is some real number.

$P(X=x) = \begin{cases}k, & \text{if } x=0\\\dfrac{k}{2}, & \text{if } x=1 \text{ or } 2\\0, & \text{otherwise}\end{cases}$

On the basis of the above information, match List-I with List-II

LIST-I		LIST-II
A. Value of $k$		I. $\dfrac{1}{4}$
B. $P(X<2)$		II. 0
C. $P(X>1)$		III. $\dfrac{1}{2}$
D. $P(X>2)$		IV. $\dfrac{3}{4}$

Choose the correct answer from the options given below:

A random variable X has the following probability distribution:

Which of the following are correct?

(A) $P(X \le 1)=0.25$

(B) $P(X>3)=0.15$

(C) $P(X=2)=0.30$

(D) $P(X \le 2)=0.55$

Choose the correct answer from the options given below:

The variance of $X$ will be :

A random variable X follows Poisson distribution. The variance of X is 2. The value of $P(X=3)$ is

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

Then, $\text{Var}\left(\frac{X}{2}\right)$ is :

10 works hard drawn successively with replacement from a lot containing 10% defective bulb. The probability that there is at least one defective bulb is :

If the sum and product of the mean and variance of a binomial distribution are 18 and 72 respectively, then the probability of obtaining atmost one success is