A random variable X has a probability distribution P(X) of the following form, where k is some unknown constant:

P(X = 0) = k

P(X = 1) = 2k

P(X = 2) = 3k

P(X = other values) = 0

Then, find the value of 1/k.

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

Choose the correct answer from the options given below:

If a random variable X follows binomial distribution with mean $\dfrac{4}{3}$ and variance $\dfrac{8}{9}$. Which of the following are correct?

A. Probability of success is $\dfrac{1}{3}$.

B. Probability of failure is $\dfrac{2}{3}$.

C. Number of trials is 4.

D. $P(X \ge 1) = \dfrac{35}{81}$

Choose the correct answer from the options given below:

If a coin is tossed 8 times and getting a head is considered as success, then which of the following statements are correct ?

(A) The probability of getting 4 heads is $\dfrac{35}{128}$

(B) The mean of the number of successes is 4.

(C) The variance of the number of successes is 2.

(D) The probability of getting 6 heads is $\dfrac{9}{64}$.

Choose the correct answer from the options given below:

The probability that a man aged 35 years will die before reaching the age of 40 years may be taken as 0.018. Out of a group of 100 men, now aged 35 years, what is the approximate probability that one man will die within next five years?

(Given: $e^{-1.8}=0.1653$)

A telephone exchange receives on an average 5 calls per minute. The probability of receiving 3 or less calls per minute is :

Match List-I with List-II

Choose the correct answer from the options given below: