$A$ boy rolls a die once. If an even number appears, the number of chocolates the boy gets is equal to two more than the number that appeared. If an odd number appears on the die, the number of chocolates he gets is equal to three more than the number that appeared. If a random variable $X$ represents the number of chocolates the boy receives, then the range of $X$ is:
- A$\{4, 6, 8\}$
- B$\{3, 5, 7\}$
- C$\{3, 4, 7\}$
- D$\{2, 3\}$
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State whether the following table represents a probability distribution of a random variable $X$. Give reasons for your answer.
$X$ $0$ $1$ $2$ $P(X)$ $0.4$ $0.4$ $0.2$
| $X$ | $0$ | $1$ | $2$ |
| $P(X)$ | $0.4$ | $0.4$ | $0.2$ |
Easy
View SolutionIf a random variable $X$ denotes the number that appears on the upper face of a die when it is rolled,then $\frac{\text{Variance of } X}{\text{Mean of } X}$ is equal to
If two dice are thrown and if $X$ denotes the sum of the numbers that show up on the faces of the dice, then the mean of the random variable $X$ is
If a random variable $X$ has the following probability distribution of $X$:
$X=x$ $0$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $P(X=x)$ $0$ $k$ $2k$ $2k$ $3k$ $k^2$ $2k^2$ $7k^2+k$
Then $P(X \geqslant 6) = $
| $X=x$ | $0$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ |
| $P(X=x)$ | $0$ | $k$ | $2k$ | $2k$ | $3k$ | $k^2$ | $2k^2$ | $7k^2+k$ |
Then $P(X \geqslant 6) = $
In a book consisting of $600$ pages, there are $60$ typographical errors. The probability that a randomly chosen page will contain at most two errors is
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