List of top Mathematics Questions on Random Variables

If $P(X=k)=c\left(\frac{2}{7}\right)^k,\ k=0,1,2,\dots$, then $P(X=2)=$

If a random variable $X$ has the following probability distribution, then the mean of $X$ is

A bookshelf contains 6 distinct books of Mathematics and 5 distinct books of Physics. From these 11 books, 6 books are chosen at random. Let $X$ be the absolute value of the difference between the number of Mathematics books chosen and the number of Physics books chosen. If $\alpha$ is the mean of the random variable $X$, then the value of $77\alpha$ is {

The c.d.f. of a discrete random variable $ X $ is Then $ P(X = -3) / P(X \leq 0) $ is:

A random variable $ X $ has p.m.f. $ P(X = x) = \frac{{}^{4}C_x}{2^4}, \quad x = 0, 1, 2, 3, 4 $, and $ \mu $ and $ \sigma^2 $ are the mean and variance respectively of the random variable $ X $, then:

Consider the probability distribution:

Then the value of $P(X > 2)$ is ______.

The cumulative distribution function of a discrete random variable X is given. Then $\frac{P(X \le 0)}{P(X > 0)} = $ ______.

A random variable X has the distribution: $P(X=1,2,3,4) = 0.1, 0.2, 0.3, 0.4$. The mean and standard deviation are:

The p.d.f. of a continuous random variable $X$ is $f(x)$.
\[ f(x)= \begin{cases} \dfrac{x^2}{18}, & -3 \le x \le 3 \\ 0, & \text{otherwise} \end{cases} \] Then find $P(|X|<2)$.

Vasant and Jothi play a game with a coin. Vasant stakes INR 1 and throws the coin four times. If he throws four heads, he gets his stake and INR3 from Jothi. If he throws only three heads and they are consecutive, he gets his stake and INR 2 from Jothi. If he throws only two heads and they are consecutive, he gets his stake and INR 1 from Jothi. In all other cases Jothi takes the stake money. Find the expectation of Vasant's gain.

The integral $ \int e^x \frac{2 + \sin 2x}{1 + \cos 2x} \, dx $ is equal to

If the vector equation of the line \[ \frac{x - 2}{2} = \frac{2y - 5}{-3} = z + 1, \] is given by: \[ \vec{r} = \left(2\hat{i} + \frac{5}{2}\hat{j} - \hat{k}\right) + \lambda\left(2\hat{i} - \frac{3}{2}\hat{j} + p\hat{k}\right), \] then $ p $ is equal to:

Let $x, y > 0$. If $x^3y^2 = 2^{15}$, then the least value of $3x + 2y$ is