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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Similar Questions
$A$ random variable $X$ has the following probability distribution:
$X$ $0$ $1$ $2$ $P(X)$ $\frac{25}{36}$ $k$ $\frac{1}{36}$
If the mean of the random variable $X$ is $\frac{1}{3}$,then the variance is:
| $X$ | $0$ | $1$ | $2$ |
|---|---|---|---|
| $P(X)$ | $\frac{25}{36}$ | $k$ | $\frac{1}{36}$ |
If the mean of the random variable $X$ is $\frac{1}{3}$,then the variance is:
MediumKCET 2024
View SolutionThe probability distribution of a random variable $X$ is given below:
$X=k$ $0$ $1$ $2$ $3$ $4$ $P(X=k)$ $0.1$ $0.4$ $0.3$ $0.2$ $0$
The variance of $X$ is:
| $X=k$ | $0$ | $1$ | $2$ | $3$ | $4$ |
|---|---|---|---|---|---|
| $P(X=k)$ | $0.1$ | $0.4$ | $0.3$ | $0.2$ | $0$ |
The variance of $X$ is:
If $P(X = x) = 5r^x$, $x = 1, 2, 3, \dots$ is the probability mass function of a discrete random variable $X$, then $r = $
Let $X$ denote the sum of the numbers obtained when two fair dice are rolled. Find the variance and standard deviation of $X$.
Difficult
View SolutionIn a game,$3$ coins are tossed. $A$ person is paid ₹ $100$,if he gets all heads or all tails; and he is supposed to pay ₹ $40$,if he gets one head or two heads. The amount he can expect to win/lose on an average per game in (₹) is
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