4. Consider a fair six-sided die with side numbers {1, 1, 1, 2, 2, 3}, i.e. three 1's,two 2' s and one 3. Assume you roll the die twice, and define the random variable X to represent the sum of the two rolls. Find the probability mass function (PMF) of X.
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- A jar contains 12 coins: 6 pennies, 2 nickels and 4 dimes. A child selects 2 coins at random without replacement from the jar. Let X be the sum of the value of the 2 coins. Determine the probability distribution of X. Please enter the values for x in increasing order. Round your answers to three decimal places, if necessary. Hint: If you are picking two different coins, remember that you can pick one first, then the other or the other way around, and you will still end up with the same two coins. X A. P(X = x) 2 0.227 6 10 0.015 11 15 20 .091 If you were to randomly draw two coins from this jar, how many cents do you expect to have on average? (Averages of discrete things CAN be decimals!)The probability that a person in the United States has type B+ blood is 10%. Three unrelated people in the United States are selected at random. Complete parts (a) through (d). (a) Find the probability that all three have type B+ blood. The probability that all three have type B+ blood is nothing. (Round to six decimal places as needed.)Suppose that we draw three cards (with replacement) from astandard deck containing 52 cards. Let X be the number of black cards drawn. Construct the probability distribution function of X as a function.
- Consider the random variable L, the length of time it takes to hear a case in a small claims court. Assume that the probability function for L is a constant, c, over the interval 20 to 120 minutes. a. Find the probability that it will take more than an hour to hear a case. b. Find the probability that it will take exactly 1 hour to hear a case.Assume that adults with smartphones are randomly selected, 48% use them in meetings or classes. If 10 adult smartphone users are randomly selected, find the probability that fewer than 4 of them use their smartphone in meetings or classes. The probability is? Round to four decimal places as needed.following random 2. Let W be a random variable giving 1. Classify variables as discrete or continuous a. X: the number of automobile accidents per year in EDSA b. Y: the length of time to paly 18 holes of golf. c. M: the amount of eggs laid each month by a hen. d.P: the number of building permits issued each month in Camiling, the the number of heads minus the number of tails in three tosses of a coin. a. List all elements of the sample space S for the three tosses of the coin and to each sample point assign a value w of W. b. Find the probability distribution of the random variable W, assuming that the coin is biased so that a head is twice as likely Tarlac e. Q: the weight of grain produces per hectare. to occur as a tail. c. Compute for value, variance and standard deviation variabe W. the expected of the random
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- ANSWERS ALL PARTS A,B,C A) Roll a dice, X=the number obtained. Calculate E(X), Var(X). Use two expressions to calculate variance. B) Two fair dice are tossed, and the face on each die is observed. Y=sum of the numbers obtained in 2 rolls of a dice. Calculate E(Y), Var(Y). C) Roll the dice 3 times, Z=sum of the numbers obtained in 3 rolls of a dice. Calculate E(Z), Var(Z) from the result of part a and b.A jar contains 12 coins: 6 pennies, 2 nickels and 4 dimes. A child selects 2 coins at random without replacement from the jar. Let X be the sum of the value of the 2 coins. Determine the probability distribution of X. Please enter the values for x in increasing order. Round your answers to three decimal places, if necessary. Hint: If you are picking two different coins, remember that you can pick one first, then the other or the other way around, and you will still end up with the same two coins. X P(X = x) 2 0.015 If you were to randomly draw two coins from this jar, how many cents do you expect to have on average? (Averages of discrete things CAN be decimals!)A platter contains 48 doughnuts: 26 cake, 13 glazed, and nine jelly-filled. Suppose two doughnuts are randomly selected in succession without replacement. Find the probability (to 4 decimal places) of selecting two cake doughnuts. A. 0.0691 B. 0.2881 C. 0.2934 D. 0.5417