The probability distribution of a random variable X is given by
$\mathrm{X=}x_i$: | 0 | 1 | 2 | 3 | 4 |
---|---|---|---|---|---|
$\mathrm{P(X=}x_i)$ : | 0.4 | 0.3 | 0.1 | 0.1 | 0.1 |
Then the variance of X is
Three houses are available in a locality. Three persons apply for the houses. Each applies for one house without consulting others. The probability that all the three persons apply for the same house is
A bag contains 4 Red and 6 Black balls. A ball is drawn at random from the bag, its colour is observed and this ball along with 3 additional balls of the same colour are returned to the bag. If now a ball is drawn at random from the bag, then the probability that this drawn ball is red is
If a discrete random variable X takes values $0,1,2,3, \ldots \ldots$. with probability $\mathrm{P}(\mathrm{X}=x)=\mathrm{k}(x+1) 5^{-x}$, where k is a constant, then $\mathrm{P}(\mathrm{X}=0)$ is