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

X	-2	2	5
P(X=x)	\(\frac{1}{4}\)	\(\frac{1}{4}\)	\(\frac{1}{2}\)

then find 4E(X²)- Var (2X)

A random variable. X has following distribution

X	-1	0	1	2
P(X=x)	\(\frac{1}{3}\)	\(\frac{1}{6}\)	\(\frac{1}{6}\)	\(\frac{1}{3}\)

Find E(2X+3)²

If a continuous random variable. X has the p.d.f. f(x) = 4k(x-1)³, 1 ≤ x ≤ 3 then find p[-2 ≤ X ≤ 2]

A player tosses two unbiased coins. He wins Rs. 5 if two heads appear, Rs. 2 if one head appear and Rs.1 if no head appear. Find the expected amount to win.

If the probability density function of a random variable. X is given by f(x) = \(\frac{2x}{9}\),0

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.

Find the probability mass function and the cumulative disttibution function for getting 3's when 2 dice are thrown,

If \(f(x)= \begin{cases}\frac{A}{x} & 1<x<e^{\prime} \\ 0 & \text { elsewhere }\end{cases}\) is a probability density function of a continuous random variable X, find f(x>e).

The total life time (in year) of 5 years old dog of a certain breed is a random variable whose distribution function is given by \(F(x)= \begin{cases}0 & x \leq 5 \\ 1-25 / x^{2} & \text { for } x>5^{\circ}\end{cases}\). Find the probability that such a five year old dog will Iive
(i) beyond 10 years
(ii) less than 8 years
(iii) anywhere between 12 to 15 years

Find the probability distribution of the number of sixes in throwing three dice once.

Two cards are drawn sucessively without replacement from a well shuffled pack of 52 cards. Find the probability distribution of queens.