Probability Questions

The variance ${\sigma }^2$ of a random variable $X$ is given by:

A coin is tossed $5$ times. The probability of head is $\frac{1}{2}$. The probability of exactly $2$ heads is:

A card is drawn at random from a pack of $52$ cards. What is the probability that the card drawn is either an Ace or a King?

The mean of the probability distribution function given by the following table will be:\begin{center}\begin{tabular}{|c|c|c|c|c|c|}\hline$x$ & 1 & 2 & 3 & 4 & 5 \ \hline$P(x)$ & 0.2 & 0.35 & 0.25 & 0.15 & 0.05 \ \hline\end{tabular}\end{center}

Given that $x$ is a random variable in the range $[0,\infty )$ with a probability density function $f(x)=\frac{e^{-x/2}}{K}$, the value of the constant $K$ is:

For a continuous random variable $X$ distributed in the interval $[0,10]$, the probability $P(X=2)$ is: