The receipe for constructing a certain random variable (k) is as follows. Take 3 (unfair) coins and toss them. For each "heads",add 1. For each "tails", add zero.There are 8 ways the coins can land. The corresponding sequence of heads and tails , the value of k, and the value of P(k)are as follows:Sequence000Value of kP(k)1/64Any of 100, 010, 001Any of 110, 101, 01111119/6427/6427/ 64(a) Verify that P(k) is positive or zero for all k.(b) Verify that P(k) is normalized.(c) What is the mean value of the random variable, k? i.e. What is (k)?(d) What is the variance of k?(e) What is the standard deviation of k?

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The receipe for constructing a certain random variable (k) is as follows. Take 3 (unfair) coins and toss them. For each “heads" add 1. For each "tails", add zero. There are 8 ways the coins can land. The corresponding sequence of heads and tails , the value of k, and the value of P(k) are as follows: Sequence Value of k P(k) 000 1/64 Any of 100, 010, 001 Any of 110, 101, 011 9/64 27/64 111 3 27/ 64 (a) Verify that P(k) is positive or zero for all k. (b) Verify that P(k) is normalized. (c) What is the mean value of the random variable k? ie VWhat is (k?

The receipe for constructing a certain random variable (k) is as follows. Take 3 (unfair) coins and toss them. For each “heads" add 1. For each "tails", add zero. There are 8 ways the coins can land. The corresponding sequence of heads and tails , the value of k, and the value of P(k) are as follows: Sequence Value of k P(k) 000 1/64 Any of 100, 010, 001 Any of 110, 101, 011 9/64 27/64 111 3 27/ 64 (a) Verify that P(k) is positive or zero for all k. (b) Verify that P(k) is normalized. (c) What is the mean value of the random variable k? ie VWhat is (k?

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Concept explainers

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.

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Question

The receipe for constructing a certain random variable (k) is as follows. Take 3 (unfair) coins and toss them. For each "heads",
add 1. For each "tails", add zero.
There are 8 ways the coins can land. The corresponding sequence of heads and tails , the value of k, and the value of P(k)
are as follows:
Sequence
000
Value of k
P(k)
1/64
Any of 100, 010, 001
Any of 110, 101, 011
111
1
9/64
27/64
27/ 64
(a) Verify that P(k) is positive or zero for all k.
(b) Verify that P(k) is normalized.
(c) What is the mean value of the random variable, k? i.e. What is (k)?
(d) What is the variance of k?
(e) What is the standard deviation of k?

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