Question

Suppose I roll a standard 6-sided die twice. Let x = the largest value of the two rolls. (a) Create a tabular p.d.f listing all possible outcomes of the experiment along with all outcome probabilities. (b) Find the mean and standard deviation of x. (c) What is the probability that x is at least 5?

Answer 1

The question involves rolling a 6-sided die twice, defining X as the largest roll, and solving for X's p.d.f, mean, standard deviation, and the chance of X being at least 5.

Step-by-step explanation:

The question at hand involves rolling a standard 6-sided die twice and defining the random variable X as the largest value obtained from the two rolls. To address this question:

1. We need to create a tabular probability distribution function (p.d.f) for all possible outcomes of the experiment and their associated probabilities.
2. Determine the mean and standard deviation of the random variable X.
3. Calculate the probability that X is at least 5.

As there are 36 possible outcomes when rolling a pair of dice, we would list these along with the probabilities of getting each largest value (1 through 6). To find the mean (μ) and standard deviation (σ), we would use the definitions of expected value and standard deviation for discrete random variables, utilizing the probabilities from the p.d.f. Finally, to find the probability that X is at least 5, we would sum the probabilities of X being 5 and 6 from our probability distribution table.