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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The following is the p.d.f. of a continuous random variable $X$: $f(x) = \begin{cases} \frac{x}{8} & , \text{if } 0 < x < 4 \\ 0 & , \text{otherwise} \end{cases}$
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Then $F(0.5)$,$F(1.7)$,and $F(5)$ are respectively:
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:
DifficultMHT CET 2026
View SolutionIf a Poisson variate $X$ satisfies the relation $P(X=3)=P(X=5)$, then $P(X=4)=$
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$X$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $P(X=x)$ $0.15$ $0.23$ $0.12$ $0.10$ $0.20$ $0.08$ $0.07$ $0.05$
For the events $E = \{X \text{ is a prime number}\}$ and $F = \{X < 4\}$,find $P(E \cup F)$.
| $X$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ |
|---|---|---|---|---|---|---|---|---|
| $P(X=x)$ | $0.15$ | $0.23$ | $0.12$ | $0.10$ | $0.20$ | $0.08$ | $0.07$ | $0.05$ |
For the events $E = \{X \text{ is a prime number}\}$ and $F = \{X < 4\}$,find $P(E \cup F)$.
If a cubical die is thrown,then the mean and variance of the random variable $X$,representing the number on the face that shows up,are respectively:
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