If the probability density function of a continuous random variable $X$ is $f(x) = \frac{x^3}{3}$ for $-1 < x < 2$,and $f(x) = 0$ otherwise,then the cumulative distribution function $F(x)$ for $-1 < x < 2$ is:
- A$\frac{1}{14}(x^4 - 1)$
- B$\frac{1}{10}(x^4 - 1)$
- C$\frac{1}{12}(x^4 - 1)$
- D$\frac{1}{16}(x^4 - 1)$
Explore More
Similar Questions
If the function $f$ defined by $f(x) = \begin{cases} K(x-x^2) & \text{if } 0 < x < 1 \\ 0 & \text{otherwise} \end{cases}$ is the probability density function (p.d.f.) of a random variable $X$,then the value of $P(X < \frac{1}{2})$ is
If $X$ is a Poisson variate such that $\alpha = P(X=1) = P(X=2)$,then $P(X=4)$ is equal to
India plays two matches each with West Indies and Australia. In any match,the probabilities of India getting $0, 1,$ and $2$ points are $0.45, 0.05,$ and $0.50$ respectively. Assuming that the outcomes are independent,the probability of India getting at least $7$ points is:
DifficultIIT 1992
View SolutionAn unbiased die is tossed until a number greater than $4$ appears. The probability that an even number of tosses is needed is
DifficultIIT 1994
View SolutionThree rotten apples are accidentally mixed with fifteen good apples. Assuming the random variable $X$ to be the number of rotten apples in a draw of two apples,the variance of $X$ is
DifficultJEE MAIN 2024
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