State which of the following is not the probability distribution of a random variable. Give reasons for your answer.
$Z$ $3$ $2$ $1$ $0$ $-1$ $P(Z)$ $0.3$ $0.2$ $0.4$ $0.1$ $0.05$
| $Z$ | $3$ | $2$ | $1$ | $0$ | $-1$ |
| $P(Z)$ | $0.3$ | $0.2$ | $0.4$ | $0.1$ | $0.05$ |
(N/A) For a probability distribution of a random variable,two conditions must be satisfied:
$1$. Each probability $P(Z_i)$ must be $\ge 0$.
$2$. The sum of all probabilities $\sum P(Z_i)$ must be equal to $1$.
In the given table,the sum of probabilities is:
$\sum P(Z) = 0.3 + 0.2 + 0.4 + 0.1 + 0.05 = 1.05$.
Since the sum of probabilities is $1.05$,which is not equal to $1$,the given table does not represent a probability distribution of a random variable.
$1$. Each probability $P(Z_i)$ must be $\ge 0$.
$2$. The sum of all probabilities $\sum P(Z_i)$ must be equal to $1$.
In the given table,the sum of probabilities is:
$\sum P(Z) = 0.3 + 0.2 + 0.4 + 0.1 + 0.05 = 1.05$.
Since the sum of probabilities is $1.05$,which is not equal to $1$,the given table does not represent a probability distribution of a random variable.
Explore More
Similar Questions
The probability distribution of random variable $X$ is given by:
$X$ $1$ $2$ $3$ $4$ $5$ $P(X)$ $K$ $2K$ $2K$ $3K$ $K$
Let $p=P(1 < X < 4 \mid X < 3)$. If $5p = \lambda K$,then $\lambda$ is equal to .... .
| $X$ | $1$ | $2$ | $3$ | $4$ | $5$ |
| $P(X)$ | $K$ | $2K$ | $2K$ | $3K$ | $K$ |
Let $p=P(1 < X < 4 \mid X < 3)$. If $5p = \lambda K$,then $\lambda$ is equal to .... .
$A$ boy tosses a fair coin $3$ times. If he gets $₹ 2x$ for $x$ heads,then his expected gain equals to $₹........$
The p.d.f. of a discrete random variable $X$ is defined as $f(x) = \begin{cases} kx^2, & x \in \{0, 1, 2, 3, 4, 5, 6\} \\ 0, & \text{otherwise} \end{cases}$. Then the value of $F(4)$ (c.d.f.) is:
If the probability function of a random variable $X$ is defined by $P(X=k) = a \left( \frac{k+1}{2^k} \right)$ for $k = 0, 1, 2, 3, 4, 5$,then the probability that $X$ takes a prime value is
DifficultAP EAMCET 2018
View SolutionSuppose the number of accidents occurring on a highway in each day follows a Poisson random variable with parameter $3$. Then,what is the probability that no accidents occur today?
DifficultAP EAMCET 2020
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