$A$ die is rolled. If $X$ denotes the number of positive divisors of the outcome,then the range of the random variable $X$ is
- A$\{1, 2, 3\}$
- B$\{1, 2, 3, 4\}$
- C$\{1, 2, 3, 4, 5, 6\}$
- D$\{1, 3, 5\}$
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$A$ box contains $8$ batteries, of which $3$ are defective. If a person randomly selects $2$ batteries from this box, find the probability distribution of the number of defective batteries $X$.
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View SolutionAn urn contains $5$ red and $2$ black balls. Two balls are randomly drawn. Let $X$ represent the number of black balls. What are the possible values of $X?$ Is $X$ a random variable?
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View SolutionIf $f(x) = \begin{cases} 3(1 - 2x^2) & ; 0 < x < 1 \\ 0 & ; \text{otherwise} \end{cases}$ is a probability density function of $X$,then $P\left(\frac{1}{4} < x < \frac{1}{3}\right)$ is
If the probability function of a random variable $X$ is given by $P(X=n) = \frac{k(n+1)}{3^n}$ for $n \in \mathbb{N} \cup \{0\}$ where $k$ is a constant, then $P(X < 2) = $
The distribution of a random variable $X$ is given below. The value of $k$ is:
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| $X = x$ | $-2$ | $-1$ | $0$ | $1$ | $2$ | $3$ |
| $P(X = x)$ | $\frac{1}{10}$ | $k$ | $\frac{1}{5}$ | $2k$ | $\frac{3}{10}$ | $k$ |
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