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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
(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
(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
(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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