Question 1 A discrete random variable X has the following probability distribution: 77 78 79 80 81 P(x) 0. 15 0. 15 0.20 0.40 0. 10 Compute each of the following quantities. a)P(80). b)P(X > 80). c)P(X = 80). d) The mean u of X. e) The variance o' of X. f) The standard deviation o of X. Question 2 Three fair dice are rolled at once. Let X denote the number of dice that land with the same number of dots on top as at least one other die. The probability distribution for X is X o 3 P(X) P 15/36 1/36 a) Find the missing value u of X. b) Find the missing probability p. c) Compute the mean of X. d) Compute the standard deviation of X. Question Three Two fair dice are rolled at once. Let X denote the difference in the number of dots that appear on the top faces of the two dice. Thus for example if a one and a five are rolled, X = 4, and if two sixes are rolled, X = 0. a)Construct the probability distribution for X. b)Compute the mean u of X. c)Compute the standard deviation o of X.Question 4 Suppose you have an experiment where you flip a coin four times. You then count the number of heads. a.) State the random variable. b.) Write the probability distribution for the number of heads. c.) Draw a histogram for the number of heads. d.) Find the mean number of heads. e.) Find the variance for the number of heads. f.) Find the standard deviation for the number of heads. g.) Find the probability of having two or more number of heads. h.) Is it unusual for to flip two heads