In a meeting,$70 \%$ of the members favour and $30 \%$ oppose a certain proposal. $A$ member is selected at random. We take $X=0$ if he opposes the proposal and $X=1$ if the member is in favour. Then the variance of $X$ is:
- A$0.21$
- B$0.23$
- C$0.25$
- D$0.27$
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The cumulative distribution function $F(x)$ of a discrete random variable $X$ is given by the following table:
$X = x$ $-1$ $0$ $1$ $2$ $F(X = x)$ $0.3$ $0.7$ $0.8$ $1$
Then $E(X^2) = $
| $X = x$ | $-1$ | $0$ | $1$ | $2$ |
|---|---|---|---|---|
| $F(X = x)$ | $0.3$ | $0.7$ | $0.8$ | $1$ |
Then $E(X^2) = $
The probability distribution of a random variable $X$ is given by
$X = x$ $0$ $1$ $2$ $P(X = x)$ $\frac{1}{5}$ $\frac{2}{5}$ $\frac{2}{5}$
Then the variance of $X$ is
| $X = x$ | $0$ | $1$ | $2$ |
| $P(X = x)$ | $\frac{1}{5}$ | $\frac{2}{5}$ | $\frac{2}{5}$ |
Then the variance of $X$ is
If $f(x) = \frac{x}{8}$ for $0 < x < 4$ and $f(x) = 0$ otherwise,is the probability density function (p.d.f.) of a continuous random variable $X$,and $F(x)$ is the cumulative distribution function (c.d.f.) associated with $f(x)$,then find $F(0.5)$.
If a discrete random variable $X$ has the probability distribution as follows:
$X = x$ $0$ $1$ $2$ $3$ $P(X = x)$ $k$ $3k$ $3k$ $k$
Then $Var(X) = $
| $X = x$ | $0$ | $1$ | $2$ | $3$ |
| $P(X = x)$ | $k$ | $3k$ | $3k$ | $k$ |
Then $Var(X) = $
For the probability distribution given by
$x = x_{i}$ $0$ $1$ $2$ $P_{i}$ $\frac{25}{36}$ $\frac{5}{18}$ $\frac{1}{36}$
the standard deviation $(\sigma)$ is
| $x = x_{i}$ | $0$ | $1$ | $2$ |
| $P_{i}$ | $\frac{25}{36}$ | $\frac{5}{18}$ | $\frac{1}{36}$ |
the standard deviation $(\sigma)$ is
MediumKCET 2018
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