The p.m.f. of a random variable $X$ is $P(x) = \begin{cases} \frac{2x}{n(n+1)}, & x = 1, 2, 3, \ldots, n \\ 0, & \text{otherwise} \end{cases}$,then $E(X)$ is
- A$\frac{n+1}{6}$
- B$\frac{2n+1}{6}$
- C$\frac{n+1}{3}$
- D$\frac{2n+1}{3}$
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$A$ fair die with numbers $1$ to $6$ on its faces is thrown. Let $X$ denote the number of factors of the number on the uppermost face. Then the probability distribution of $X$ is
For the following probability distribution,the standard deviation of the random variable $X$ is:
$X$ $2$ $3$ $4$ $P(X=x)$ $0.2$ $0.5$ $0.3$
| $X$ | $2$ | $3$ | $4$ |
|---|---|---|---|
| $P(X=x)$ | $0.2$ | $0.5$ | $0.3$ |
$A$ fair die is tossed twice in succession. If $X$ denotes the number of fours in $2$ tosses,then the probability distribution of $X$ is given by
DifficultMHT CET 2023
View SolutionIf 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:
The variance of the following probability distribution is:
$x$ $0$ $1$ $2$ $P(X)$ $\frac{9}{16}$ $\frac{3}{8}$ $\frac{1}{16}$
| $x$ | $0$ | $1$ | $2$ |
|---|---|---|---|
| $P(X)$ | $\frac{9}{16}$ | $\frac{3}{8}$ | $\frac{1}{16}$ |
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