$A$ coin is tossed twice in succession. Let $X$ represent the number of tails in two tosses,then the probability distribution of $X$ is given by
- A
$X=x_i$ $0$ $1$ $2$ $P_i$ $1/2$ $1/4$ $1/4$ - B
$X=x_i$ $0$ $1$ $2$ $P_i$ $1/3$ $1/3$ $1/3$ - C
$X=x_i$ $0$ $1$ $2$ $P_i$ $1/4$ $1/4$ $1/2$ - D
$X=x_i$ $0$ $1$ $2$ $P_i$ $1/4$ $1/2$ $1/4$
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State which of the following is not the probability distribution of a random variable. Give reasons for your answer.
$Z$ $3$ $2$ $1$ $0$ $-1$ $P(Z)$ $0.3$ $0.2$ $0.4$ $0.1$ $0.05$
| $Z$ | $3$ | $2$ | $1$ | $0$ | $-1$ |
| $P(Z)$ | $0.3$ | $0.2$ | $0.4$ | $0.1$ | $0.05$ |
Easy
View SolutionLet $F(x)$ be the cumulative distribution function (c.d.f.) of a continuous random variable $X$. If $F(b) = 0.7$ and $P(X > a) = 0.4$, then the value of $P(a < X < b)$ is ...
DifficultMHT CET 2026
View Solution$A$ 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) = $
From a well-shuffled pack of $52$ playing cards,cards are drawn one by one with replacement. The probability that the $5^{th}$ card will be the "king of hearts" is:
$A$ player tosses two coins. He wins $Rs. 1$ if $1$ head appears,$Rs. 2$ if $2$ heads appear. But he loses $Rs. 3$ if no head appears. The mean of the prize money is
DifficultAP EAMCET 2017
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