If $f(x) = \frac{x+2}{18}$ for $-2 < x < 4$ and $f(x) = 0$ otherwise,is the probability density function (p.d.f.) of a random variable $X$,then the value of $P(|X| < 2)$ is
- A$\frac{5}{9}$
- B$\frac{4}{9}$
- C$\frac{2}{9}$
- D$\frac{1}{9}$
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$A$ coin is biased so that the head is $3$ times as likely to occur as tail. This coin is tossed until a head or three tails occur. If $X$ denotes the number of tosses of the coin,then the mean of $X$ is
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Let $X$ denote the sum of the numbers obtained when two fair dice are rolled. Find the variance and standard deviation of $X$.
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View Solution$A$ random variable $X$ has the following distribution.
$X = x_{i}$ $-2$ $-1$ $0$ $1$ $2$ $3$ $P(X = x_{i})$ $0.1$ $k$ $0.2$ $2k$ $3k$ $k$
Then the variance of this distribution is
| $X = x_{i}$ | $-2$ | $-1$ | $0$ | $1$ | $2$ | $3$ |
| $P(X = x_{i})$ | $0.1$ | $k$ | $0.2$ | $2k$ | $3k$ | $k$ |
Then the variance of this distribution is
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