1.) Let \( \Omega \) be a deck of cards. Define a random variable \( X \) such that for any card \( c \) in the deck\[X(c) = \begin{cases} \text{the number value on the card for all numbered cards} \\10 \text{ for any face cards (jack, queen, king)} \\11 \text{ for any ace}\end{cases}\]What is \( \mathbb{E}[X] \)?

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Answered: 1.) Let 2 be a deck of cards. Define a…

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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A deck consists of 32 cards with 2 suits labelled A and B, and numbered ranks from 1 to 16. That is, there are 16 cards of each suit and 2 cards of each rank. A single card is chosen at random from the deck. What is the probability of it being rank 7 given that it is suit b? And What is the probability of it being suit b given that it has rank 7?
8.) Six letters of the alphabet are chosen at random. Find the probability that the following "words" are formed: (a) REDSOX (b) A "word" that ends in Y (c) A "word" with no repeated letters (d) A "word" that does not contain A,B, or C
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Six digits are chosen randomly from the set {0, 1,2,.....9). a.) What is the probability that all six digits are the same? b.) What is the probability that only 2 digits are the same?
11.) A shipment of 11 printers contains 2 that are defective. Find the probability that a sample of 4, drawn from the 11, will not contain a defective printer.
Teachers want to know which night each week their students are doing most of their homework. Most teachers think that students do homework equally throughout the week. Suppose a random sample of students were collected which shows that the Number of students doing their homework on SUN where 16 Number of students doing their homework on MON where 18 Number of students doing their homework on TUE where 12 Number of students doing their homework on WED where 18 Number of students doing their homework on THR where 8 Number of students doing their homework on FRI where 4 Number of students doing their homework on SAT where 3 What is the Test Statistics to test the Hull Hypothesis that students were doing their homework with equal frequencies (that is, they fit a uniform distribution) against the alternative Hypothesis that students prefer doing their homework on a particular day (that is, they do not fit a uniform distribution)?
A card is randomly drawn from a deck of well-shuffled playing cards. Let event E be that the card is a king and event F be that the card is a diamond. A standard 52-card deck is split evenly into four suits of cards (hearts, diamonds, clubs, and spades). Each suit contains the cards ace, 2, 3.., 10, jack, queen, king. a) Find P(E) and P (E'). b) Find P(F) and P (F'). c) Find P(EUF).

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1.) Let 2 be a deck of cards. Define a random variable X such that for any card e in the deck the number value on the card for all numbered cards 10 for any face cards (jack, queen, king) 11 for any ace X(e) = What is E(X)?