Statistics and Probability Cmtent: Random Variable, Discrete Distribution, and Normal Distribution Direction: Solve the following worded problems. Part 1. Random Variable ' 1. A pair of 4sided dice is rolled, and the sum is determined. Let the random variable X denotes the sum of the numbers. Find the sample space, write the values of the random variable, determine the probability mass function, and draw the histogram. Determine also the probability that the sum is a) prime number, b) even number, and c) composite number. Part 2. Mean, Variance, and Standard Deviation of Discrete Distribution- 2. The discrete random variable X has the probability distribution shown below. X -2 D 1 3 P(X=x) 0.32 0.27 a 0.24 Calculate a. the value of a b. E(X) c. 50;\") d. E(2X + 5) e. Var(X) f. Var(3x 8) Part 3. Normal Distribution 3A. 3. BIOLOGY: The average number, per country, of an endangered Bald Eagle (Ham bucocepr'rar'us) is 9.8 with a standard deviation 0.6. Find the probabilities ofthe following with illustrated gaussian curve. a. P(6