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
For the given probability distribution,find $E(X^2)$.$X$ $1$ $2$ $3$ $4$ $P(X)$ $\frac{1}{10}$ $\frac{1}{5}$ $\frac{3}{10}$ $\frac{2}{5}$
| $X$ | $1$ | $2$ | $3$ | $4$ |
| $P(X)$ | $\frac{1}{10}$ | $\frac{1}{5}$ | $\frac{3}{10}$ | $\frac{2}{5}$ |
The cumulative distribution function (c.d.f.) $F(x)$ associated with the probability density function (p.d.f.) $f(x) = 3(1 - x^2)$ for $0 < x < 1$ and $f(x) = 0$ otherwise,is given by $F(x) = k(x - \frac{2x^3}{k})$. Find the value of $k$.
If the probability distribution of a random variable $X$ is as follows,then $k=$
$X=x$ $1$ $2$ $3$ $4$ $P(X=x)$ $2k$ $4k$ $3k$ $k$
(in $/10$)
| $X=x$ | $1$ | $2$ | $3$ | $4$ |
| $P(X=x)$ | $2k$ | $4k$ | $3k$ | $k$ |
The c.d.f. $F(x)$ associated with the p.d.f. $f(x)$ is given by:
$f(x) = \begin{cases} 12x^2(1-x), & \text{if } 0 < x < 1 \\ 0, & \text{otherwise} \end{cases}$
$f(x) = \begin{cases} 12x^2(1-x), & \text{if } 0 < x < 1 \\ 0, & \text{otherwise} \end{cases}$
If the probability that an individual will suffer a bad reaction from an injection is $0.001$, then the probability that out of $2000$ individuals, exactly $3$ individuals suffer a bad reaction is
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