91Ó°ÊÓ

What is the difference between a discrete random variable and a continuous random variable? Provide your own examples of each.

True or False: In the binomial probability distribution function, \({ }_{n} \mathrm{C}_{x}\) represents the number of ways of obtaining \(x\) successes in \(n\) trials.

Determine whether the random variable is discrete or continuous. In each case, state the possible values of the random variable. (a) The number of light bulbs that burn out in the next week in a room with 20 bulbs. (b) The time it takes to fly from New York City to Los Angeles. (c) The number of hits to a website in a day. (d) The amount of snow in Toronto during the winter.

The expected number of successes in a binomial experiment with \(n\) trials and probability of success \(p\) is ______.

Determine whether the random variable is discrete or continuous. In each case, state the possible values of the random variable. (a) The amount of rain in Seattle during April. (b) The number of fish caught during a fishing tournament. (c) The number of customers arriving at a bank between noon and 1: 00 P.M. (d) The time required to download a file from the Internet.

Determine whether the random variable is discrete or continuous. In each case, state the possible values of the random variable. (a) The number of defects in a roll of carpet. (b) The distance a baseball travels in the air after being hit. (c) The number of points scored during a basketball game. (d) The square footage of a house.

The random variable \(X\) follows a Poisson process with the given value of \(\lambda\) and \(t\). Assuming \(\lambda=0.07\) and \(t=10\), compute (a) \(P(4)\) (b) \(P(X<4)\) (c) \(P(X \geq 4)\) (d) \(P(4 \leq X \leq 6)\) (e) \(\mu_{X}\) and \(\sigma_{X}\)

Determine which of the following probability experiments represents a binomial experiment. If the probability experiment is not a binomial experiment, state why. An experimental drug is administered to 100 randomly selected individuals, with the number of individuals responding favorably recorded.

Determine whether the distribution is a discrete probability distribution. If not, state why. $$ \begin{array}{cc} x & P(x) \\ \hline 0 & 0.2 \\ \hline 1 & 0.2 \\ \hline 2 & 0.2 \\ \hline 3 & 0.2 \\ \hline 4 & 0.2 \\ \hline \end{array} $$

Determine whether the distribution is a discrete probability distribution. If not, state why. $$ \begin{array}{ll} x & P(x) \\ \hline 0 & 0.1 \\ \hline 1 & 0.5 \\ \hline 2 & 0.05 \\ \hline 3 & 0.25 \\ \hline 4 & 0.1 \\ \hline \end{array} $$