In a meeting,$70 \%$ of the members favour and $30 \%$ oppose a certain proposal. $A$ member is selected at random and we take $X=0$ if he opposed,and $X=1$ if he is in favour. Find $E(X)$ and $\text{Var}(X)$.
- A$0.7, 0.21$
- B$0.7, 0.49$
- C$0.3, 0.21$
- D$0.3, 0.09$
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Similar Questions
State which of the following is not a probability distribution of a random variable. Give reasons for your answer.
$X$ $0$ $1$ $2$ $3$ $4$ $P(X)$ $0.1$ $0.5$ $0.2$ $-0.1$ $0.3$
| $X$ | $0$ | $1$ | $2$ | $3$ | $4$ |
| $P(X)$ | $0.1$ | $0.5$ | $0.2$ | $-0.1$ | $0.3$ |
Easy
View SolutionWhich of the following can not be a valid assignment of probabilities for outcomes of sample space $S = \{\omega_{1}, \omega_{2}, \omega_{3}, \omega_{4}, \omega_{5}, \omega_{6}, \omega_{7}\}$?
Outcome Probability $\omega_{1}$ $0.1$ $\omega_{2}$ $0.01$ $\omega_{3}$ $0.05$ $\omega_{4}$ $0.03$ $\omega_{5}$ $0.01$ $\omega_{6}$ $0.2$ $\omega_{7}$ $0.6$
| Outcome | Probability |
| $\omega_{1}$ | $0.1$ |
| $\omega_{2}$ | $0.01$ |
| $\omega_{3}$ | $0.05$ |
| $\omega_{4}$ | $0.03$ |
| $\omega_{5}$ | $0.01$ |
| $\omega_{6}$ | $0.2$ |
| $\omega_{7}$ | $0.6$ |
Easy
View SolutionSuppose 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 Solution$A$ random variable $X$ has the following probability distribution:
$X = x$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $P(X = x)$ $0.15$ $0.23$ $k$ $0.10$ $0.20$ $0.08$ $0.07$ $0.05$
For the events $E = \{x : x \text{ is a prime number}\}$ and $F = \{x : x < 4\}$,then $P(E \cup F) = $
| $X = x$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ |
| $P(X = x)$ | $0.15$ | $0.23$ | $k$ | $0.10$ | $0.20$ | $0.08$ | $0.07$ | $0.05$ |
For the events $E = \{x : x \text{ is a prime number}\}$ and $F = \{x : x < 4\}$,then $P(E \cup F) = $
$A$ random variable $X$ has the following probability distribution. Find the value of $k$ and the value of $P(3 < X \leq 6)$.
$X = x$ $0$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $P(x)$ $k$ $2k$ $3k$ $4k$ $4k$ $3k$ $2k$ $k$ $k$
| $X = x$ | $0$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ |
|---|---|---|---|---|---|---|---|---|---|
| $P(x)$ | $k$ | $2k$ | $3k$ | $4k$ | $4k$ | $3k$ | $2k$ | $k$ | $k$ |
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