A random variable \(X\) has the following probability distribution : x 0 1 2 3 4 P(x) k 2k 4k 6k 8k
The value of \(P(1 < X < 4 | x ≤ 2)\) is equal to
| x | 0 | 1 | 2 | 3 | 4 |
| P(x) | k | 2k | 4k | 6k | 8k |
The value of \(P(1 < X < 4 | x ≤ 2)\) is equal to
- \(\frac{4}{7}\)
- \(\frac{2}{3}\)
- \(\frac{3}{7}\)
- \(\frac{4}{5}\)
The Correct Option is A
Solution and Explanation
\(∵ \;x \) is a random variable
\(∴\; k + 2k + 4k + 6k + 8k = 1\)
\(∴\; k =\frac{1}{21}\)
Then, \(P(1<x<4)|x<=2)\)
=\(\frac{4k}{7k}\)
= \(\frac{4}{7}\)
Hence, the correct option is (A): \(\frac{4}{7}\)
Top Questions on Random Variables
- If the vector equation of the line \[ \frac{x - 2}{2} = \frac{2y - 5}{-3} = z + 1, \] is given by: \[ \vec{r} = \left(2\hat{i} + \frac{5}{2}\hat{j} - \hat{k}\right) + \lambda\left(2\hat{i} - \frac{3}{2}\hat{j} + p\hat{k}\right), \] then \( p \) is equal to:
- MHT CET - 2024
- Mathematics
- Random Variables
- The integral \( \int e^x \frac{2 + \sin 2x}{1 + \cos 2x} \, dx \) is equal to
- MHT CET - 2024
- Mathematics
- Random Variables
A force \(F =\left(5+3 y^2\right)\) acts on a particle in the \(y\)-direction, where \(F\) is in newton and \(y\) is in meter The work done by the force during a displacement from \(y=2 m\) to \(y=5 m\) is___ \(J\).
- JEE Main - 2023
- Physics
- Random Variables
A random sample of size $5$ is taken from the distribution with density \[ f(x;\theta)= \begin{cases} \dfrac{3x^2}{\theta^3}, & 0[6pt] 0, & \text{elsewhere}, \end{cases} \] where $\theta$ is unknown. If the observations are $3,6,4,7,5$, then the maximum likelihood estimate of the $1/8$ quantile of the distribution (rounded off to one decimal place) is __________.
- GATE ST - 2022
- Estimation
- Random Variables
- Let $0,1,1,2,0$ be five observations of a random variable $X$ which follows a Poisson distribution with parameter $\theta>0$. Let the minimum variance unbiased estimate of $P(X\le 1)$, based on this data, be $\alpha$. Then $5^{4}\alpha$ (in integer) is equal to $\;__________$
- GATE ST - 2022
- Estimation
- Random Variables
Questions Asked in JEE Main exam
- For two identical cells each having emf \(E\) and internal resistance \(r\), the current through an external resistor of \(6\,\Omega\) is the same when the cells are connected in series as well as in parallel. The value of the internal resistance \(r\) is ________ \(\Omega\).
- JEE Main - 2026
- Current electricity
- For three unit vectors \( \vec a, \vec b, \vec c \) satisfying \[ |\vec a-\vec b|^2 + |\vec b-\vec c|^2 + |\vec c-\vec a|^2 = 9 \] and \[ |2\vec a + k\vec b + k\vec c| = 3, \] the positive value of \( k \) is:
- JEE Main - 2026
- Vector Algebra
In the given figure, the blocks $A$, $B$ and $C$ weigh $4\,\text{kg}$, $6\,\text{kg}$ and $8\,\text{kg}$ respectively. The coefficient of sliding friction between any two surfaces is $0.5$. The force $\vec{F}$ required to slide the block $C$ with constant speed is ___ N.
(Given: $g = 10\,\text{m s}^{-2}$)
- JEE Main - 2026
- Rotational Mechanics
- The system of linear equations
$x + y + z = 6$
$2x + 5y + az = 36$
$x + 2y + 3z = b$
has- JEE Main - 2026
- Matrices and Determinants
Method used for separation of mixture of products (B and C) obtained in the following reaction is:
- JEE Main - 2026
- p -Block Elements
Concepts Used:
Random Variable
A random variable is a variable whose value is unknown or a function that assigns values to each of an experiment's results. Random variables are often deputed by letters and can be classified as discrete, which are variables that have particular values, or continuous, which are variables that can have any values within a continuous range.
Random variables are often used in econometric or regression analysis to ascertain statistical relationships among one another.
Types of Random Variable
There are two types of random variables, such as:
- Discrete Random Variable - A discrete random variable can take only a finite number of unique values such as 0, 1, 2, 3, 4, … and so on. The probability distribution of a random variable has a list of probabilities differentiated with each of its possible values known as the probability mass function.
- Continuous Random Variable - An arithmetically valued variable is said to be continuous if, in any unit of measurement, whenever it can take on the values a and b. If the random variable X can presume an infinite and uncountable set of values, it is said to be a continuous random variable. When X takes any value in a given interval (a, b), it is also known to be a continuous random variable in that interval.