The p.d.f. of a random variable $x$ is given by $f(x) = \frac{1}{4a}$ for $0 < x < 4a$ $(a > 0)$ and $f(x) = 0$ otherwise. If $P(x < \frac{3a}{2}) = k P(x > \frac{5a}{2})$,then $k = . . . . . .$
- A$1$
- B$\frac{1}{2}$
- C$\frac{1}{8}$
- D$\frac{3}{2}$
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Similar Questions
The probability distribution of a random variable $X$ is given by the following table:
$X = x$ $1$ $2$ $3$ $\dots$ $n$ $P(X = x)$ $\frac{1}{n}$ $\frac{1}{n}$ $\frac{1}{n}$ $\dots$ $\frac{1}{n}$
Then $\operatorname{Var}(X) = $
| $X = x$ | $1$ | $2$ | $3$ | $\dots$ | $n$ |
|---|---|---|---|---|---|
| $P(X = x)$ | $\frac{1}{n}$ | $\frac{1}{n}$ | $\frac{1}{n}$ | $\dots$ | $\frac{1}{n}$ |
Then $\operatorname{Var}(X) = $
If a random variable $X$ denotes the number that appears on the upper face of a die when it is rolled,then $\frac{\text{Variance of } X}{\text{Mean of } X}$ is equal to
If the mean of a Poisson distribution is $\frac{1}{2}$,then the ratio of $P(X=3)$ to $P(X=2)$ is
Let a sample space be $S = \{\omega_{1}, \omega_{2}, \ldots, \omega_{6}\}$. Which of the following assignments of probabilities to each outcome is valid?
Outcome Probability $\omega_{1}$ $1/8$ $\omega_{2}$ $2/3$ $\omega_{3}$ $1/3$ $\omega_{4}$ $1/3$ $\omega_{5}$ $-1/4$ $\omega_{6}$ $-1/3$
| Outcome | Probability |
|---|---|
| $\omega_{1}$ | $1/8$ |
| $\omega_{2}$ | $2/3$ |
| $\omega_{3}$ | $1/3$ |
| $\omega_{4}$ | $1/3$ |
| $\omega_{5}$ | $-1/4$ |
| $\omega_{6}$ | $-1/3$ |
Easy
View SolutionIf the probability distribution of a random variable $X$ is given by:
$X = x_i$ $0$ $1$ $2$ $3$ $P(X = x_i)$ $\frac{1}{8}$ $\frac{3}{8}$ $3K$ $K$
Find the variance of $X$.
| $X = x_i$ | $0$ | $1$ | $2$ | $3$ |
|---|---|---|---|---|
| $P(X = x_i)$ | $\frac{1}{8}$ | $\frac{3}{8}$ | $3K$ | $K$ |
Find the variance of $X$.
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