If the following function is a probability density function of a random variable $X$, $f(x) = kx^2(1 - x)$ for $0 < x < 1$ and $f(x) = 0$ otherwise, then the value of $k$ is:
- A$-12$
- B$\frac{1}{12}$
- C$\frac{1}{6}$
- D$12$
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If $X$ is a Poisson variate such that $\alpha = P(X=1) = P(X=2)$, then $P(X=4)$ is equal to
$A$ random variable $X$ has the following probability distribution:
$X = x$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $P(X = x)$ $0.15$ $0.23$ $k$ $0.10$ $0.20$ $0.08$ $0.07$ $0.05$
For the events $E = \{x : x \text{ is a prime number}\}$ and $F = \{x : x < 4\}$, then $P(E \cup F) = $
| $X = x$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ |
| $P(X = x)$ | $0.15$ | $0.23$ | $k$ | $0.10$ | $0.20$ | $0.08$ | $0.07$ | $0.05$ |
For the events $E = \{x : x \text{ is a prime number}\}$ and $F = \{x : x < 4\}$, then $P(E \cup F) = $
$A$ random variable $X$ has the following probability distribution:
$X$: $1, 2, 3, 4$
$P(X)$: $0.2, 0.4, 0.3, 0.1$
The mean and variance of $X$ are respectively:
$X$: $1, 2, 3, 4$
$P(X)$: $0.2, 0.4, 0.3, 0.1$
The mean and variance of $X$ are respectively:
If the probability distribution of a random variable $X$ is as follows,then $P(X \leq 2) = $ $x_i$ $0$ $1$ $2$ $3$ $4$ $P(X = x_i)$ $3K$ $5K$ $3k^2$ $4k^2 + k$ $3k^2$
| $x_i$ | $0$ | $1$ | $2$ | $3$ | $4$ |
|---|---|---|---|---|---|
| $P(X = x_i)$ | $3K$ | $5K$ | $3k^2$ | $4k^2 + k$ | $3k^2$ |
For the following probability distribution,the standard deviation of the random variable $X$ is:
$X$ $2$ $3$ $4$ $P(X=x)$ $0.2$ $0.5$ $0.3$
| $X$ | $2$ | $3$ | $4$ |
|---|---|---|---|
| $P(X=x)$ | $0.2$ | $0.5$ | $0.3$ |
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