Practice section 1 of 7

Two fair tetrahedral dice, each with faces 1, 2, 3 and 4, are thrown. The score is the sum of their two numbers. Let $X$ denote the score. Find the probability distribution of $X$.

The discrete random variable $Y$ has probability distribution

Find (i) $d$, (ii) $P(-3\le Y<0)$ and (iii) $P(Y>-1)$.

$X$ has probability mass function $P(X=x)=c(4/5)^x$ for integers $x\ge0$. Find (i) $c$ and (ii) $P(X\ge3)$.

Find $c$ such that the following is a probability distribution, then find $P(|X-\frac12|>\frac14)$.

$P(X=x)=\begin{cases}cx^2,&x=-1,-\frac12,\\x,&x=0,\\cx,&x=\frac34,1,\\0,&\text{otherwise}.\end{cases}$

The random variable $Y$ has distribution

If $V=Y^2$, find the probability distribution of $V$.

The discrete random variable $X$ has distribution

Find the mode and median of $X$.