The p.d.f. of a continuous random variable $X$ is given by $f(x) = \frac{1}{2}$ if $0 < x < 2$ and $f(x) = 0$ otherwise. If $a = P(X < \frac{1}{2})$ and $b = P(X > \frac{3}{2})$,then the relation between $a$ and $b$ is:
- A$a - b = 0$
- B$2a - b = 0$
- C$3a - b = 0$
- D$a - 2b = 0$
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Similar Questions
$A$ random variable $X$ has the following probability distribution:
$X = x_i$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $P(X = x_i)$ $10k$ $9k$ $8k$ $8k$ $6k$ $5k$ $4k$ $3k$ $k$
where $k$ is a real number. If $A = \{ x_i : x_i \text{ is a prime number} \}$ and $B = \{ x_i : x_i > 5 \}$ are two events, then $P(A \cup B) = $
| $X = x_i$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ |
| $P(X = x_i)$ | $10k$ | $9k$ | $8k$ | $8k$ | $6k$ | $5k$ | $4k$ | $3k$ | $k$ |
where $k$ is a real number. If $A = \{ x_i : x_i \text{ is a prime number} \}$ and $B = \{ x_i : x_i > 5 \}$ are two events, then $P(A \cup B) = $
For the following cumulative distribution function $F(x)$ of a random variable $X$,find $P(3 < X \leq 5)$.
$x$ $1$ $2$ $3$ $4$ $5$ $6$ $F(x)$ $0.2$ $0.37$ $0.48$ $0.62$ $0.85$ $1$
| $x$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ |
|---|---|---|---|---|---|---|
| $F(x)$ | $0.2$ | $0.37$ | $0.48$ | $0.62$ | $0.85$ | $1$ |
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 $k$.
Suppose the number of accidents occurring on a highway in each day follows a Poisson random variable with parameter $3$. Then,what is the probability that no accidents occur today?
DifficultAP EAMCET 2020
View SolutionThe number of persons joining a cinema ticket counter in a minute follows a Poisson distribution with parameter $\lambda = 6$. The probability that at least one and at most five persons join the queue in a particular minute is:
DifficultAP EAMCET 2023
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