The discrete random variable X has the probability function

X	1	2	3	4
P(X=x)	k	2k	3k	4k

Show that k = 0.1.

Define random variable.

What do you understand by continuous random variable?

What are the properties of
(i) discrete random variable and
(ii) continuous random variable?

Find the expected value for the random variable of an unbiased die

Determine whether the following is a probability distribution of a random variable X.

X	0	1	2
P(X)	0.6	0.1	0.2

An unbiased die is rolled. If the random variable X is defined as
X(w) = {1, the outcome w is an even number    
{0, if the outcome w is an odd number
Find the probability distribution of X.

Two eggs are drawn at random without replacement from a bag containing two bad eggs and eight good eggs. Find the probability of getting two bad eggs?

A random variable X has the probability mass function

X	-2	3	1
P(X=x)	\(\frac{k}{6}\)	\(\frac{k}{4}\)	\(\frac{k}{12}\)

then find k

A discrete random variable. X has the following probability distribution

X	0	1	2	3	4	5	6	7	8
P(X)	a	3a	5a	7a	9a	11a	13a	15a	17a

Pind the value of a and P(X< 3)

Verify whether \(f(x)=\begin{cases} \frac { 2x }{ 9 } ,\quad 0\le x\le \\ 0,\quad elsewhere \end{cases}\) is a probability density function

A continuous random variable. X has the p.d.f. defined by \(f(x)=\left\{\begin{array}{l} C e^{-a x}, \quad 0<x<\infty \\ 0, \quad \text { elsewhere } \end{array}\right.\) Find the value of C if a> 0

In an entrance examination a student has to answer all the 120 questions. Each question has four options and only one option is correct. A student gets 1 mark for a correct answer and loses \(\frac{1}{2}\) mark for a wrong answer. What is the expectation of the mark scored by a student if he chooses the answer to each question at random?

In a gambling game a man wins Rs. 10 if he gets all heads or all tails and loses Rs. 5 if he gets 1 or 2 heads when 3 coins are tossed once. Find his expectation of gain.

Find the mean for the probability density function \(f(x)=\begin{cases} \frac { 1 }{ 24 } ,-12\le x\le 12 \\ 0,\quad otherwise \end{cases}\)