Question Type 2: Finding the standard deviation of a discrete random variable Exercises

The probability mass function of $X$ is given by $P(X=1)=0.2$, $P(X=2)=0.5$, and $P(X=3)=0.3$.

Calculate the standard deviation of $X$.

A discrete random variable $X$ takes values 0 and 2 with equal probability. Find the standard deviation of $X$. [4 marks]

A loaded die is rolled once. The probability of face $i$ is $P(i)=i/21$ for $i=1,2,3,4,5,6$. Find the standard deviation of the outcome $X$.

Let $X$ take values $1, 2, 3, 4, 5$ with $P(X=x)=k(6-x)$. Determine $k$ and compute the standard deviation of $X$.

A random variable $X$ has the probability mass function $P(X=x)=kx$ for $x \in \{1, 2, 3, 4\}$.

Find the value of $k$ and the standard deviation of $X$.

Let $X$ have pmf $P(X=x)=\frac{c}{x^2}$ for $x=1,2,3$. Determine $c$ and compute $\text{Var}(X)$.

The pmf of $X$ is $P(X=1)=\frac{1}{6}$, $P(X=2)=\frac{1}{3}$, $P(X=3)=\frac{1}{2}$. Find the variance of $X$ and its standard deviation.

Let $X$ be a discrete random variable that takes the values $0$, $1$ and $3$ with probabilities $p$, $2p$ and $1-3p$ respectively. Given that $\text{E}(X)=1$, find the value of $p$ and the standard deviation of $X$.

A discrete random variable $X$ has probability mass function $P(X=x) = \frac{6}{11} \cdot \frac{1}{x}$ for $x = 1, 2, 3$.

Find $\text{Var}(X)$.

A random variable $X$ has probability distribution given by $P(X=-1)=0.2$, $P(X=0)=0.5$, $P(X=2)=0.3$. Find $\text{Var}(X)$.

Let $X$ be uniformly distributed on $\{0, 1, 2\}$. Find the standard deviation of $X$.

Let $X$ have pmf $P(X=x)=k\,3^x$ for $x=0,1,2$. Determine $k$ and find the standard deviation of $X$.