The following is the p.d.f. of a continuous random variable $X$: $f(x) = \begin{cases} \frac{x}{8} & , \text{if } 0 < x < 4 \\ 0 & , \text{otherwise} \end{cases}$
Then $F(0.5)$,$F(1.7)$,and $F(5)$ are respectively:
Then $F(0.5)$,$F(1.7)$,and $F(5)$ are respectively:
- A$\frac{1}{64}, 1, 0.18$
- B$0.0156, 0.18, 1$
- C$0.18, 0.0156, 1$
- D$1, 0.0156, 0.18$
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Similar Questions
$A$ random variable $X$ has the following probability distribution:
$X$ $0$ $1$ $2$ $3$ $4$ $5$ $6$ $P(X)$ $k$ $3k$ $5k$ $7k$ $9k$ $11k$ $13k$
Then find $P(X \ge 2)$.
| $X$ | $0$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ |
|---|---|---|---|---|---|---|---|
| $P(X)$ | $k$ | $3k$ | $5k$ | $7k$ | $9k$ | $11k$ | $13k$ |
Then find $P(X \ge 2)$.
If the probability function of a discrete random variable $X$ is $P(X=r) = r/k$ for $r = 1, 2, 3, 4, 5$, then $P(X=2 \text{ or } X=k/3)$ is equal to:
Given below is the distribution of a random variable $X$:
$X=x$ $1$ $2$ $3$ $4$ $P(X=x)$ $\lambda$ $2\lambda$ $3\lambda$ $4\lambda$
If $\alpha=P(X < 3)$ and $\beta=P(X>2)$,then $\alpha: \beta=$
| $X=x$ | $1$ | $2$ | $3$ | $4$ |
| $P(X=x)$ | $\lambda$ | $2\lambda$ | $3\lambda$ | $4\lambda$ |
If $\alpha=P(X < 3)$ and $\beta=P(X>2)$,then $\alpha: \beta=$
If $P(X = x) = 5r^x$, $x = 1, 2, 3, \dots$ is the probability mass function of a discrete random variable $X$, then $r = $
If $X$ is a random variable with cumulative distribution function $F(x)$ and its probability distribution is given by the following table:
$X = x$ $-1.5$ $-0.5$ $0.5$ $1.5$ $2.5$ $P(X = x)$ $0.05$ $0.2$ $0.15$ $0.25$ $0.35$
Then,find the value of $F(1.5) - F(-0.5)$.
| $X = x$ | $-1.5$ | $-0.5$ | $0.5$ | $1.5$ | $2.5$ |
|---|---|---|---|---|---|
| $P(X = x)$ | $0.05$ | $0.2$ | $0.15$ | $0.25$ | $0.35$ |
Then,find the value of $F(1.5) - F(-0.5)$.
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