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 random variable X has a probability distribution P(X) of the following form where k is a scalar and

$P(X = x) = \begin{cases} k, & \text{if } x = 0 \\ 2k, & \text{if } x = 1 \\ 3k, & \text{if } x = 2 \\ 0, & \text{otherwise} \end{cases}$

then value of P(X < 2) = _______.

Which of the following statements are correct ?

(A) $\text{var}(aX + b) = a^2 \text{var}(X)$

(B) $\text{var}(X) = E(X^2) - \{E(X)\}^2$

(C) $E(aX + b) = aE(X) + b$

(D) $E(X) = \sum_{i=1}^{n} p_i x_i^2$

Choose the correct answer from the options given below :

If X is a Poisson variate such that $3P(X=2)=2P(X=1)$, then $P(X=0)$ is equal to: (Given $e^{-4/3}=0.264$)

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

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

2 voices dice are thrown together. For the first die $P(6) = \frac{1}{2}$, other scores are equally likely. While for the second die $P(1) = \frac{2}{5}$ and other scores are equally likely than the Mean for the probability distribution of the number of one score will be

The probability distribution of a discrete random variable X is given by :

then E(X) is equals to