The number of computers sold per day at Dan's Computer Works...

The number of computers sold per day at Dan's Computer Works is defined by the following probability distribution: $$ \begin{array}{lccccccc} \hline x & 0 & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline P(x) & 0.05 & 0.10 & 0.20 & 0.20 & 0.20 & 0.15 & 0.10 \\ \hline \end{array} $$ a. $P(3 \leq x<6)=$ ? b. $P(x>3)=$ ? c. $P(x \leq 4)=$ ? d. $P(2<x \leq 5)=$ ?

The number of computers sold per day at Dan's Computer Works is defined by the following probability distribution:
$$
\begin{array}{lccccccc}
\hline x & 0 & 1 & 2 & 3 & 4 & 5 & 6 \\
\hline P(x) & 0.05 & 0.10 & 0.20 & 0.20 & 0.20 & 0.15 & 0.10 \\
\hline
\end{array}
$$
a. $P(3 \leq x<6)=$ ?
b. $P(x>3)=$ ?
c. $P(x \leq 4)=$ ?
d. $P(2<x \leq 5)=$ ?

Key Concepts

Range Probability Calculation

Range probability calculation involves finding the probability that a discrete random variable falls within a specified range. This is typically done by adding the probabilities of all individual outcomes within that range. This concept is used when dealing with conditions such as 'x < 6' or 'x ? 3', and requires careful interpretation of the inequality symbols to sum the appropriate probabilities from the distribution.

Cumulative Probability

Cumulative probability refers to the probability that a random variable takes a value less than or equal to a certain number. This is obtained by summing the individual probabilities for all outcomes up to that number. It is an important concept for determining the likelihood that a random variable will fall within a specific cumulative range.

Probability Distribution

A probability distribution assigns a probability to each possible outcome of a discrete random variable. For a valid probability distribution, the sum of the probabilities of all possible outcomes must equal 1. It provides a complete description of the likelihood of each outcome and is the basis for calculating probabilities over specified ranges or events.

Discrete Random Variable

A discrete random variable is a type of variable that can only take on a countable number of distinct values. It is often associated with countable outcomes, such as the number of computers sold in a day. Understanding discrete random variables is fundamental because their analysis involves summing individual probabilities for each specific possible outcome.

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