The random variable $X$ has a probability distribution $P(X)$ of the following form,where $k$ is some number:
$P(X) = \begin{cases} k, & \text{if } x=0 \\ 2k, & \text{if } x=1 \\ 3k, & \text{if } x=2 \\ 0, & \text{otherwise} \end{cases}$
Determine the value of $k$.
$P(X) = \begin{cases} k, & \text{if } x=0 \\ 2k, & \text{if } x=1 \\ 3k, & \text{if } x=2 \\ 0, & \text{otherwise} \end{cases}$
Determine the value of $k$.
- A$1/6$
- B$1/3$
- C$1/2$
- D$1$
Explore More
Similar Questions
Suppose that a random variable $X$ follows a Poisson distribution. If $P(X=1) = P(X=2)$, then $P(X=5)$ is equal to:
The cumulative distribution function $F(X)$ of a discrete random variable $X$ is given by the following table:
$X$ $1$ $2$ $3$ $4$ $5$ $6$ $F(X=x)$ $0.2$ $0.37$ $0.48$ $0.62$ $0.85$ $1$
Then $P[X=4] + P[X=5] = $
| $X$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ |
|---|---|---|---|---|---|---|
| $F(X=x)$ | $0.2$ | $0.37$ | $0.48$ | $0.62$ | $0.85$ | $1$ |
Then $P[X=4] + P[X=5] = $
$A$ random variable $X$ has the probability distribution given below. Its variance is:
$X$ $1$ $2$ $3$ $4$ $5$ $P(X=x)$ $K$ $2K$ $3K$ $2K$ $K$
| $X$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $P(X=x)$ | $K$ | $2K$ | $3K$ | $2K$ | $K$ |
If the probability distribution function of a random variable $X$ is given as follows:
$X=x_i$ $-2$ $-1$ $0$ $1$ $2$ $P(X=x_i)$ $0.2$ $0.3$ $0.15$ $0.25$ $0.1$
Then $F(0)$ is equal to:
| $X=x_i$ | $-2$ | $-1$ | $0$ | $1$ | $2$ |
|---|---|---|---|---|---|
| $P(X=x_i)$ | $0.2$ | $0.3$ | $0.15$ | $0.25$ | $0.1$ |
Then $F(0)$ is equal to:
Consider a game of tossing a six-sided fair die. If the face that comes up is $k$, the player wins Rs. $36/k$ and loses Rs. $2k$, where $k \in \{1, 2, 3, 4, 5, 6\}$. What is the expected winning amount in this game in Rs.?
DifficultMHT CET 2026
View SolutionVedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo