Please solve three different parts for a,b and c. Thank you. Hunch.Two dice are rolled. Let X = 1 if the dice come up doubles and letX 0otherwise. Let Y = 1 if the sum is 6, and let Y = 0 otherwise. Let Z 1 if the dice comeup both doubles and with a sum of 6 (that is, doublé 3), and let Z = 0 otherwise.a.Let pX denote the success probability for X. Find pX,uX,oXb.Let pY denote the success probability for Y.Find pY,. uY,oYC.Let pz denote the success probability for Z. Find pzuz,oz4

Answered: Two dice are rolled. Let X 1 if the…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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Please solve three different parts for a,b and c. Thank you.

Hunch.
Two dice are rolled. Let X = 1 if the dice come up doubles and letX 0
otherwise. Let Y = 1 if the sum is 6, and let Y = 0 otherwise. Let Z 1 if the dice come
up both doubles and with a sum of 6 (that is, doublé 3), and let Z = 0 otherwise.
a.
Let pX denote the success probability for X. Find pX,uX,oX
b.Let pY denote the success probability for Y.Find pY,. uY,oY
C.
Let pz denote the success probability for Z. Find pzuz,oz
4

Expert Solution

Step 1

a) X denotes the event that dice comes up doubles.

Possible combinations of doubles in a throw of 2 dice = $(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)$

Therefore, Probability of success for X = $p_{x} = \frac{6}{36} = \frac{1}{6}$

The probability distribution of X is given by:

$\begin{matrix} X & 0 & 1 \\ P (X) & \frac{5}{6} & \frac{1}{6} \end{matrix}$

Therefore,

$μ_{x} = E (X) = 0 \times \frac{5}{6} + 1 \times \frac{1}{6} = \frac{1}{6}$

$E (X^{2}) = 0 \times \frac{5}{6} + 1^{2} \times \frac{1}{6} = \frac{1}{6} σ_{x} = E (X^{2}) - {(E (X))}^{2} = \frac{1}{6} - {(\frac{1}{6})}^{2} = \frac{5}{36}$

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