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:

In a binomial distribution the probability of getting success is $\frac{1}{4}$ And standard deviation is 3 then its mean is ?

If the random variable X follows the Poisson distribution such that P[X = k] = P[X = k+1], then the mean value of X is:

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 has a Poisson distribution such that $2P(X=1)=P(X=2)$, then which of the following are correct?

A. The mean of X is 4

B. The mean of X is 2

C. $P(X=2)=\frac{8}{e^4}$

D. $P(X=3)=\frac{32}{e^4}$

Choose the correct answer from the options given below:

The number of telephone calls made daily in a certain community between 8 P.M. and 9 P.M. has a mean of 352 and standard deviation of 31. What percentage of time will there be more than 400 telephone calls made in this community between 8 P.M. to 9 P.M.?

[Given that: $P(0\leq Z\leq1.55)=0.4394$, where $Z$ is the standard normal variate]

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

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