For the following probability distribution of a random variable $X$, the Expected value $E(X)$ and Variance $Var(X)$ of $X$ are respectively: $X=x$ $1$ $2$ $3$ $P(X=x)$ $1/5$ $2/5$ $2/5$
| $X=x$ | $1$ | $2$ | $3$ |
| $P(X=x)$ | $1/5$ | $2/5$ | $2/5$ |
- A$27/5, 27/25$
- B$11/5, 14/25$
- C$4/5, 14/25$
- D$7/5, 11/25$
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The probability distribution of a discrete random variable $X$ is given below: $X = x$ $-1$ $0$ $1$ $2$ $P(X = x)$ $\frac{1}{3}$ $\frac{1}{6}$ $\frac{1}{6}$ $\frac{1}{3}$
Then the value of $6 \Sigma(x^2) P(X=x) - \operatorname{var}(X) =$ ?
| $X = x$ | $-1$ | $0$ | $1$ | $2$ |
|---|---|---|---|---|
| $P(X = x)$ | $\frac{1}{3}$ | $\frac{1}{6}$ | $\frac{1}{6}$ | $\frac{1}{3}$ |
Then the value of $6 \Sigma(x^2) P(X=x) - \operatorname{var}(X) =$ ?
$A$ random variable $X$ has the following probability distribution:
$X = x$ $0$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $P(X = x)$ $0$ $k$ $2k$ $2k$ $3k$ $k^2$ $2k^2$ $7k^2 + k$
Then $F(4) = $
| $X = x$ | $0$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ |
|---|---|---|---|---|---|---|---|---|
| $P(X = x)$ | $0$ | $k$ | $2k$ | $2k$ | $3k$ | $k^2$ | $2k^2$ | $7k^2 + k$ |
Then $F(4) = $
If a random variable $X$ follows a Poisson distribution such that $P(X=1) = 3P(X=2)$, then $P(X=3) =$
If a Poisson variate $X$ satisfies $P(X=2) = P(X=3)$, then $P(X=5) =$
An urn contains $5$ red and $2$ black balls. Two balls are randomly drawn. Let $X$ represent the number of black balls. What are the possible values of $X?$ Is $X$ a random variable?
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