Natasha Awada, Paul La Rondie, Laurie Buchanan and, Jill Stevens Solutions for Chapter: Valid Comparisons and Informed Decisions: Probability Distributions, Exercise 7: Exercise 14A

A board game is played by moving a counter $S$ spaces forward at a time, where $S$ is determined by the following rule: A fair six-sided dice is thrown once. $S$ half the number shown on the dice if that number is even; otherwise $S$ is twice the number shown on the dice. Find the probability that, in a single turn, a player moves their counter forward more than $2$ spaces.

The random variable $X$ has the probability distribution shown.

Find the value of $c$.

The random variable $X$ has the probability distribution shown.

Find $P(1 < X<4)$.

The probability distribution of a random variable $Y$ is given by: $P(Y= y) = c{y}^3$ for $y = 1, 2, 3$. Given that $c$ is a constant, find the value of $c$.

The random variable X has the probability distribution shown.

Find the value of $k$.

The random variable $X$ has the probability distribution given by $P(X=x)= k{\left(\frac{1}{3}\right)}^{x-1}$ for$x= 1, 2, 3, 4,$ where $k$ is a constant. Find the exact value of $k$.

The discrete random variable $X$ can take only the values $0, 1, 2, 3, 4, 5$. The probability distribution of $X$ is given by the following 

$P(X=0)=P(X=1)=P(X= 2) = a$

$P(X=3)=P(X=4)=P(X= 5) = b$

$P(X\ge 2)=3P(X<2)$

where $a$ and $b$ are constants.

Determine the probability that the sum of two independent observations from this distribution exceeds $7$.

The discrete random variables A and B are independent and have the following distributions.

The random variable $C$ is the sum of one observation from A and one observation from $B$. Tabulate the probability distribution for $C$.