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 $\alpha: \beta=$
- A$2 : 5$
- B$3 : 4$
- C$4 : 5$
- D$3 : 7$
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If a random variable $X$ follows a Poisson distribution such that $P(X=1) = 3P(X=2)$,then $P(X=3) =$
If the mean of a Poisson distribution is $\frac{1}{2}$,then the ratio of $P(X=3)$ to $P(X=2)$ is
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 $F(1.5) - F(-0.5)$.
The probability distribution of a random variable $X$ is given by:
$X = x_i$ $0$ $1$ $2$ $3$ $4$ $P(X = x_i)$ $0.4$ $0.3$ $0.1$ $0.1$ $0.1$
Then the variance of $X$ is:
| $X = x_i$ | $0$ | $1$ | $2$ | $3$ | $4$ |
|---|---|---|---|---|---|
| $P(X = x_i)$ | $0.4$ | $0.3$ | $0.1$ | $0.1$ | $0.1$ |
Then the variance of $X$ is:
$A$ random variable $X$ has the probability distribution given below. Its variance is:
$X$ $1$ $2$ $3$ $4$ $5$ $P(X=x)$ $K$ $2K$ $3K$ $2K$ $K$
| $X$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $P(X=x)$ | $K$ | $2K$ | $3K$ | $2K$ | $K$ |
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