If a random variable X follows poisson's distribution such that $P(X=2) = 9P(X=4) + 90P(X=6)$, then the mean of X is

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:

If a random variable X follows binomial distribution with mean 5 and variance $\frac{5}{2}$, then $P(X \leq 9)$ is :

The variance of the Binomial Distribution $B\left(5, \frac{1}{4}\right)$ is:

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.

Let $X$ be a discrete random variable whose probability distribution is defined as follows;

$P(X=x)=\begin{cases}k(x+1), & x=1,2,3,4\\ 2kx, & x=5,6,7\\ 0, & \text{otherwise}\end{cases}$

where $k$ is constant, then $P(X=5)$ is equal to

If $X$ is a Poisson variate such that $P(X=3)=2P(X=4)$, then $P(X=2)$ equals:

[given $e^{-2}=0.14$]