lease answer the question with details on how to do it. Thank you.  5.) Suppose that a coin is tossed three times so that the sample space is   S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}. Let x represent the # of heads that can come up.  Create a table for its Probability Distribution Function (PDF) and draw its histogram. Test if the sum of  probability is 1.

Renee and Thomas live at the beach and collect seashells. The number of shells Renee collects on any given day, R, is approximately Normal with a mean of 58.2 shells and a standard deviation of 12.8 shells. The number of shells Thomas collects on any given day, T, is approximately Normal with a mean of 47.9 shells and a standard deviation of 11.5 shells. Assume the two random variables are independent of each other. What is the probability that on a randomly selected day the total number of shells collected by Renee and Thomas is 120 or more? 0.002 0.209 0.284 0.791

Determine whether the value is a discrete random variable, continuous random variable, or not a random variable. a. The time required to download a file from the Internet b. The number of fish caught during a fishing tournament c. The response to the survey question "Did you smoke in the last week?" d. The distance a baseball travels in the air after being hit e. The number of hits to a website in a day f. The time it takes for a light bulb to burn out a. Is the time required to download a file from the Internet a discrete random variable, a continuous random variable, or not a random variable? C O A. It is a continuous random variable. O B. It is a discrete random variable. O C. It is not a random variable. b. Is the number of fish caught during a fishing tournament discrete random variable, a continuous random variable, or not a random variable? O A. It is a continuous random variable. O B. It is a discrete random variable. O C. It is not a random variable c. Is the response to the…

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The random variable x represents the number of emails a student receives on a day. Assume it has a Poisson distribution with a mean of 14.3 emails. Find the probability that in a random day the student receives 3 emails. Round your answer to four decimal places.