Let $X$ denote the number of hours you study on a Sunday. It is known that $P(X=x) = \begin{cases} 0.1 & \text{if } x=0 \\ kx & \text{if } x=1, 2 \\ k(5-x) & \text{if } x=3, 4 \\ 0 & \text{otherwise} \end{cases}$ where $k$ is a constant. Then the probability that you study at least two hours on a Sunday is
- A$0.55$
- B$0.15$
- C$0.75$
- D$0.3$
Explore More
Similar Questions
If a random variable $X$ has the p.d.f. $f(x) = \begin{cases} \frac{k}{x^2+1} & , \text{if } 0 < x < \infty \\ 0 & , \text{otherwise} \end{cases}$,then the c.d.f. of $X$ is:
The following table shows the probability distribution of smart phones sold in a shop per day:
Number of smart phones $(x)$ $0$ $1$ $2$ $3$ $4$ $5$ Probability $(P(x))$ $k$ $0.3$ $0.15$ $0.15$ $0.1$ $2k$
Then $E(x) = ?$
| Number of smart phones $(x)$ | $0$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|---|
| Probability $(P(x))$ | $k$ | $0.3$ | $0.15$ | $0.15$ | $0.1$ | $2k$ |
Then $E(x) = ?$
The variance of the random variable $X$ having the following distribution is:
$X = k$ $-2$ $-1$ $0$ $1$ $2$ $P(X = k)$ $\frac{1}{6}$ $\frac{1}{6}$ $\frac{1}{3}$ $\frac{1}{6}$ $\frac{1}{6}$
| $X = k$ | $-2$ | $-1$ | $0$ | $1$ | $2$ |
|---|---|---|---|---|---|
| $P(X = k)$ | $\frac{1}{6}$ | $\frac{1}{6}$ | $\frac{1}{3}$ | $\frac{1}{6}$ | $\frac{1}{6}$ |
$A$ bakerman sells $5$ types of cakes. Profit due to sale of each type of cake is respectively $Rs \ 2$,$Rs \ 2.5$,$Rs \ 3$,$Rs \ 1.5$ and $Rs \ 1$. The demands for these cakes are $20 \%$,$5 \%$,$10 \%$,$50 \%$ and $15 \%$ respectively. Then the expected profit per cake is:
Let a random variable $X$ take values $\{0, 1, 2, 3\}$ with $P(X=0) = P(X=1) = p$,$P(X=2) = P(X=3) = q$,and $E(X^2) = 2E(X)$. Then the value of $8p - 1$ is:
DifficultJEE MAIN 2025
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