1. For each 0! the lol lowing exercises. determine the range {output. possible values} oi the random variable. {a} A group of 1,000 people is tested [or 0 FthD negative blood type. The random variable is the number of people who carry this blood type. (b) Suppose 4 dioe are rolled. The random variable is the sum of the numbers. to} The random variable is the number of rainy days in Atlanta in a year. 2. The sample space of a random experiment is la, b, c, d, e, f}, and each outcome is equally likelyr {so P[X = x} = 1/ 6 for each outcome]. A random variable is defined as follows: outcome a h r. d c f . Determine the pmt and coil of X. - Calculate E00. 02 and o. 3. A life insurance companyr is selling life insurance of $16,000 for a premium of $320 per year. The table below shows that the probability of death in the year following the purchase oi this policy is 0.1%. What is the expected gain for this type of policy? Simple event Probability Gain .1' 0.999 3320 0.001 $15,680 4. Let the random variable X have a discrete uniform distribution on the integers 0 s x s 20. Determine the mean and variance of X. 5. During the 2013 regular NBA season, DeAndre Jordan of the Los Angeles Clippers had the league's highest field goal completion rate. DeAndre scored with 61.3% of his shots. Suppose you choose a random sample of 80 shots made by DeAndre during the 2013 season. Let X = the number of shots that scored points. la} What type is this probability distribution for X? lb) Using the formulas, calculate the mean and standard deviation oi X. (o) (Bonus:I Using Fl, find the probability that DeAndre scored with 50 of these shots. id] {Bonus} Using R. find the probability that DeAndre scored with more than 50 of these shots