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$0.3$
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Similar Questions
The probability distribution of a discrete random variable $X$ is given by the following table:
$X$ $1$ $2$ $3$ $4$ $5$ $6$ $P(X)$ $K$ $2K$ $3K$ $4K$ $5K$ $6K$
Find the value of $P(2 < X < 6)$.
| $X$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ |
|---|---|---|---|---|---|---|
| $P(X)$ | $K$ | $2K$ | $3K$ | $4K$ | $5K$ | $6K$ |
Find the value of $P(2 < X < 6)$.
In a book consisting of $600$ pages, there are $60$ typographical errors. The probability that a randomly chosen page will contain at most two errors is
For the following probability distribution of a random variable $X$, the Expected value $E(X)$ and Variance $Var(X)$ of $X$ are respectively: $X=x$ $1$ $2$ $3$ $P(X=x)$ $1/5$ $2/5$ $2/5$
| $X=x$ | $1$ | $2$ | $3$ |
| $P(X=x)$ | $1/5$ | $2/5$ | $2/5$ |
DifficultMHT CET 2026
View SolutionThe range of a random variable $X$ is $\{0, 1, 2\}$. If $P(X=0) = 3C^3$,$P(X=1) = 4C - 10C^2$,and $P(X=2) = 5C - 1$,then the value of $C$ is
At a telephone enquiry system,the number of phone calls regarding relevant enquiries follows a Poisson distribution with an average of $5$ phone calls during $10$-minute time intervals. The probability that there is at most one phone call during a $10$-minute time period is:
MediumAIEEE 2006
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