Say you have a biased coin and you associate obtaining a head with the value 0 whereas obtaining a tail has a value of 2. Let X be the sum of the values obtained from tossing the coin three times. (Round your answers to 4 decimal places, if needed.) (a) If the probability of getting heads in a single toss is 0.36, then what is the probability distribution of X ? x 0 2 4 6 P(X = x)         (b) What is P(X < 6)? (c) What is P(1 < X < 5)?

Q4.  Researchers developed a "dog IQ test" and find that the population of dogs in the United States has a mean score of µ = 20 on this test with a standard deviation of σ = 2. You decide to test a sample of n = 40 dogs to do some research about whether some breeds are smarter.   You decide to first test your own dog (or your closest friend's or family member's, if you don't have one). What is the probability that your dog will score an "dog IQ" greater than 25 (which is the cut-off for "Doggie Genius")?

The following are the probability distributions for the cost of textbooks in the fall semester for two different majors. Each probability represents the chance that the total cost of a student's books will be the given amount. Calculate the absolute difference in the expected cost of textbooks for the fall semester for these two majors. Express your answer rounded to two decimal places. Cost of Textbooks (in dollars) for Business Majors X 431.00 510.00 625.00 X Cost of Textbooks (in dollars) for Chemistry Majors 500.00 601.00 P(X = x) 649.00 0.23 0.56 0.21 P(X = x) 0.18 0.52 0.30

If the odds in favor of event E are a to b the probability of the event is given by P(E) = a/(a+b) Choose one of the causes of death from the article and convert odds to probability - determine the probability of this cause of death. Determine the probability that the cause of death is not the one you chose. Explain why it is so difficult to calculate this probability directly yet so easy to calculate it using a trick.You can chose which death or you can do for drowning doesnt matter.