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

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

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

The pmf of $X$ is $P(X=1)=0.2$, $P(X=2)=0.5$, $P(X=3)=0.3$. Calculate the standard deviation of $X$.

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

A random variable $X$ has pmf $P(X=-1)=0.2$, $P(X=0)=0.5$, $P(X=2)=0.3$. Compute $\mathrm{Var}(X)$.

A random variable $X$ has pmf $P(X=x)=kx$ for $x=1,2,3,4$. Find $k$ and then the standard deviation of $X$.

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

A discrete random variable $X$ has pmf $P(X=x)=\tfrac{6}{11}\cdot\tfrac{1}{x}$ for $x=1,2,3$. Find $\mathrm{Var}(X)$.

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

Suppose $X$ takes values 0, 1 and 3 with probabilities $p$, $2p$, $1-3p$ respectively. Given that $E[X]=1$, find $p$ and the standard deviation of $X$.

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 $X$.