The probability distribution of a discrete random variable $X$ is given by the following table:
$X = x$ $0$ $1$ $2$ $3$ $4$ $P(X = x)$ $k$ $2k$ $4k$ $2k$ $k$
Then the value of $P(X \leq 2)$ is:
| $X = x$ | $0$ | $1$ | $2$ | $3$ | $4$ |
| $P(X = x)$ | $k$ | $2k$ | $4k$ | $2k$ | $k$ |
Then the value of $P(X \leq 2)$ is:
- A$\frac{1}{10}$
- B$\frac{7}{10}$
- C$\frac{3}{10}$
- D$\frac{9}{10}$
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Similar Questions
$A$ random variable $X$ has the following probability density function (p.d.f.):
$f(x) = kx(1-x), 0 \leqslant x \leqslant 1$
If $P(X > a) = \frac{20}{27}$,then find the value of $a$.
$f(x) = kx(1-x), 0 \leqslant x \leqslant 1$
If $P(X > a) = \frac{20}{27}$,then find the value of $a$.
The probability distribution of a random variable $X$ is given by:
$X = x_i$ $0$ $1$ $2$ $3$ $4$ $P(X = x_i)$ $0.4$ $0.3$ $0.1$ $0.1$ $0.1$
Then the variance of $X$ is:
| $X = x_i$ | $0$ | $1$ | $2$ | $3$ | $4$ |
|---|---|---|---|---|---|
| $P(X = x_i)$ | $0.4$ | $0.3$ | $0.1$ | $0.1$ | $0.1$ |
Then the variance of $X$ is:
For the following probability distribution,the standard deviation of the random variable $X$ is:
$X$ $2$ $3$ $4$ $P(X=x)$ $0.2$ $0.5$ $0.3$
| $X$ | $2$ | $3$ | $4$ |
|---|---|---|---|
| $P(X=x)$ | $0.2$ | $0.5$ | $0.3$ |
The p.d.f. of a random variable $X$ is given by $f(x) = \frac{k}{\sqrt{x}}$ for $0 \leq x \leq 4$ and $f(x) = 0$ otherwise. Then $P(1 < X < 4) = $
The probability mass function of a random variable $X$ is given by $P(X=x) = \frac{{}^{5}C_{x}}{2^{5}}$ for $x = 0, 1, 2, 3, 4, 5$ and $0$ otherwise. Then,$P(X \leq 2)$ is equal to:
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