If a random variable. X has the probability distribution

X	0	1	2	3	4	5
P(X=x)	a	2a	3a	4a	5a	6a

then find F(4)

Let X denote the number of hours you study during a randomly selected school day. The probability distribution function is
\(P(X=x)=\begin{cases} \begin{matrix} 0.1 & if\quad x=0 \end{matrix} \\ \begin{matrix} kx & if\quad x=1\quad or\quad 2 \end{matrix} \\ \begin{matrix} k(5-x) & if\quad x=3\quad or\quad 4 \end{matrix} \\ \begin{matrix} 0, & otherwise \end{matrix} \end{cases}\)
Find the value of k and what is the probability that you study atleast 2 hours.

A random variable X can take all nonnegative integral values and the probabilities that X takes the value r is proportional to aT (0 < ∝ < 1). Find P(X = 0)

Two cards are drawn from a pack of 52 playing cards. Find the probability distribution of the number of aces.

An urn contains 4 white and 6 red balls. Four balls are drawn at random from the urn. Find the probability distribution of the number of white balls.