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(See Exercise 3 from "Problems on Random Variables and Joint Distributions") A die is rolled. Let X be the number of spots that turn up. A coin is flipped X times. Let Y be the number of heads that turn up. Determine the distribution for Y .

PX = [0 (1/6)*ones(1,6)];PY = [0.5 0.5];gend Do not forget zero coefficients for missing powersEnter gen fn COEFFICIENTS for gN PX Enter gen fn COEFFICIENTS for gY PYResults are in N, PN, Y, PY, D, PD, P May use jcalc or jcalcf on N, D, PTo view the distribution, call for gD. disp(gD) % Compare with P8-30 0.1641 1.0000 0.31252.0000 0.2578 3.0000 0.16674.0000 0.0755 5.0000 0.02086.0000 0.0026
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(See Exercise 4 from "Problems on Random Variables and Joint Distributions") As a variation of [link] , suppose a pair of dice is rolled instead of a single die. Determine the distribution for Y .

PN = (1/36)*[0 0 1 2 3 4 5 6 5 4 3 2 1];PY = [0.5 0.5];gend Do not forget zero coefficients for missing powersEnter gen fn COEFFICIENTS for gN PN Enter gen fn COEFFICIENTS for gY PYResults are in N, PN, Y, PY, D, PD, P May use jcalc or jcalcf on N, D, PTo view the distribution, call for gD. disp(gD)0 0.0269 1.0000 0.10252.0000 0.1823 3.0000 0.21584.0000 0.1954 5.0000 0.14006.0000 0.0806 7.0000 0.03758.0000 0.0140 % (Continued next page) 9.0000 0.004010.0000 0.0008 11.0000 0.000112.0000 0.0000
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(See Exercise 5 from "Problems on Random Variables and Joint Distributions") Suppose a pair of dice is rolled. Let X be the total number of spots which turn up. Roll the pair an additional X times. Let Y be the number of sevens that are thrown on the X rolls. Determine the distribution for Y . What is the probability of three or more sevens?

PX = (1/36)*[0 0 1 2 3 4 5 6 5 4 3 2 1];PY = [5/6 1/6];gend Do not forget zero coefficients for missing powersEnter gen fn COEFFICIENTS for gN PX Enter gen fn COEFFICIENTS for gY PYResults are in N, PN, Y, PY, D, PD, P May use jcalc or jcalcf on N, D, PTo view the distribution, call for gD. disp(gD)0 0.3072 1.0000 0.36602.0000 0.2152 3.0000 0.08284.0000 0.0230 5.0000 0.00486.0000 0.0008 7.0000 0.00018.0000 0.0000 9.0000 0.000010.0000 0.0000 11.0000 0.000012.0000 0.0000 P = (D>=3)*PD' P = 0.1116
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(See Example 7 from "Conditional Expectation, Regression") A number X is chosen by a random selection from the integers 1 through 20 (say by drawing a card from a box). A pair of dice is thrown X times. Let Y be the number of “matches” (i.e., both ones, both twos, etc.). Determine the distribution for Y .

gN = (1/20)*[0 ones(1,20)];gY = [5/6 1/6];gend Do not forget zero coefficients for missing powersEnter gen fn COEFFICIENTS for gN gN Enter gen fn COEFFICIENTS for gY gYResults are in N, PN, Y, PY, D, PD, P May use jcalc or jcalcf on N, D, PTo view the distribution, call for gD.disp(gD)0 0.2435 1.0000 0.26612.0000 0.2113 3.0000 0.14194.0000 0.0795 5.0000 0.03706.0000 0.0144 7.0000 0.00478.0000 0.0013 9.0000 0.000310.0000 0.0001 11.0000 0.000012.0000 0.0000 13.0000 0.000014.0000 0.0000 15.0000 0.000016.0000 0.0000 17.0000 0.000018.0000 0.0000 19.0000 0.000020.0000 0.0000
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Source:  OpenStax, Applied probability. OpenStax CNX. Aug 31, 2009 Download for free at http://cnx.org/content/col10708/1.6
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