The cumulative distribution function of a continuous random variable $X$ is given by $F(x) = \frac{\sqrt{x}}{2}$ for $0 \leq x \leq 4$. Then $P[X > 1]$ is
- A$\frac{1}{3}$
- B$\frac{1}{\sqrt{2}}$
- C$\frac{1}{2}$
- D$\frac{1}{4}$
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If $f(x) = \begin{cases} 3(1 - 2x^2) & ; 0 < x < 1 \\ 0 & ; \text{otherwise} \end{cases}$ is a probability density function of $X$,then $P\left(\frac{1}{4} < x < \frac{1}{3}\right)$ is
The variance of the random variable $X$ having the following distribution is:
$X = k$ $-2$ $-1$ $0$ $1$ $2$ $P(X = k)$ $\frac{1}{6}$ $\frac{1}{6}$ $\frac{1}{3}$ $\frac{1}{6}$ $\frac{1}{6}$
| $X = k$ | $-2$ | $-1$ | $0$ | $1$ | $2$ |
|---|---|---|---|---|---|
| $P(X = k)$ | $\frac{1}{6}$ | $\frac{1}{6}$ | $\frac{1}{3}$ | $\frac{1}{6}$ | $\frac{1}{6}$ |
$A$ random variable $X$ takes the values $0, 1, 2, 3, \dots$ with probability $P(X=x) = k(x+1)\left(\frac{1}{5}\right)^x$,where $k$ is a constant. Then $P(X=0)$ is
Let $X$ denote the sum of the numbers obtained when two fair dice are rolled. Find the variance and standard deviation of $X$.
Difficult
View Solution$A$ random variable $X$ takes values $0, 1, 2, 3, \ldots$ with probability $P(X=x) = K(x+1)\left(\frac{1}{5}\right)^x$,where $K$ is a constant. Then $P(X=0)$ is:
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