probability 1 (i) Four independent flips of a fair coin are made. Let X denote the number of heads obtained.Plot the probability mass function of the random variable X – 2.(ii) Calculate Var (X), if X represents the outcome when a fair die is rolled. Hint: E[X] = 7/2.(iii) Suppose that the distribution function of X is given by0,6 <0b/4, 0≤b<1F(b) 1/2+ [(b-1)/4], 1≤ b < 211/12, 2

"As per the Bartleby guidelines, we are entitled to solve only one question at a time.As you have…

Answered: (i) Four independent flips of a fair…

(i) Four independent flips of a fair coin are made. Let X denote the number of heads obtained. Plot the probability mass function of the random variable X - 2.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Related questions

Q: A doctor gives a patient a 80% chance of surviving bypass surgery after a heart attack. If the…

Q: Selecting Marbles A bag contains 9 red marbles, 6 white marbles, and 5 blue marbles. Randomly choose…

A: No.of red marbles=9No.of white marbles=6No.of blue marbles=5Total marbles=20

Q: Fourteen people apply for a teaching position in mathematics at a local college. Eight have a PhD…

A: M=8, N=14, n=5 X~HG(5,14,8)

Q: qustion 2 part (b) Two dices are rolled. What is the probability that (i) T he sum of two numbers…

Q: A two-digit number is formed from the numbers (0,1,2.3,4.5,6) without repetition. What is the…

A: Solution: A two digit number is formed from the number 0,1,2,3,4,5 and 6. without repeating the…

Q: Selecting Marbles A bag contains 5 red marbles, 8 white marbles, and 7 blue marbles. Randomly choose…

Q: A fair die is rolled three times. What is the probability of obtaining at least two 5's? P(at least…

Q: (2) Two girls and four boys sit in a row, then the probability that the two girls sit together is…

A: PTwo girls sit together=Number of ways two girls can sit togetherTotal number of ways 2 girlsa nd 4…

Q: Selecting Marbles A bag contains 5 red marbles, 6 white marbles, and 9 blue marbles. Randomly choose…

A: From the provided information,A bag contains 5 red marbles, 6 white marbles, and 9 blue…

Q: Five people (Alex, Bill, Cathy, David, and Erica) form a club, N= {A, B, C, D, E}. Cathy and Erica…

A: Given, There are 5 people, these are Alex, Bill, Cathy, David, Erica.

Q: Binomial Probability 1. Assume a hotel has 5 elevators and one of the elevators is a freight…

Q: Find the probability that a point on SK is not on PK. Answer as a fraction in simplist form. TH P. R…

A: From the given figure, Distance between P and K is equal to 10-2=8 Distance between S and K is equal…

Q: 10.lf two dice are rolled one time, find the probability of getting a sum of 6 or 9.

Q: Cash Transaction No Check Total Check Make The given table indicates the transactions for one teller…

A: Given data: Transaction Cash Check No Check Total Make Deposit 28 20 48 Withdraw 26 10 36…

Q: Notation Assume that we want to find the probability that when five consumers are randomly selected,…

A: From the information, five consumers are randomly selected, 42% of consumers are comfortable with…

Q: Use the statement, if p(E) = a/b, then o(E) = a:(b - a) and o(E') = (b- a):a, to find the odds that…

Q: Method Total ways to count? # successful outcomes? Probability? combination

A: We know that There are 52 cards in the deck divided into two colour i.e red( 26) and black (26). The…

Q: Three identical dice are thrown. Find the probability of getting sum at most 16.

A: Solution: From the given information, three identical dice are thrown.

Q: (a) Compute the probability of randomly selecting a club or heart. (b) Compute the probability of…

A: The experiment is of a standard deck of cards. Total no. of cards = 52 One card can be selected from…

Q: States Infection Recovery A 5677 1276 B 716 10 C 695 303 Based on the result, find…

Q: The table gives a set of outcomes and their probabilities. Let A be the event "the outcome is a…

A: Given,"A" be the event "the outcome is a divisor of 4"B be the event "the outcome is prime "possible…

Q: (a) Suppose that you throw 3 dice. Find the probability that you get at least one 3. (b) Suppose…

A: There are 3 dice rolled, tge sample space in one dice are { 1,2,3,4,5,6} .Without 3 the sample space…

Q: A family has 5 children and the probability of having a girl is Find the probability that the family…

Q: Two dice are rolled. Then the probability of getting a

A: When two dice are rolled then, total number of outcomes is equal to 36. P(event) = desired…

Q: What is the probability a random employee of this company is a drug user? Find: P(T and D) =…

A: From the conclusions we see, P(T|D) = 0.93 P(T|Dc) = 0.05 P(Tc| Dc) = 1 – 0.05 = 0.95 P(T) = 0.19…

Q: O You are dealt two cards successively (without replacement) from a shuffled deck of numbered cards…

A: Given that Total people selected (n) = 1114 Regular smokers = 162 Heavy smokers = 93 both heavy and…

Q: Selecting Marbles A bag contains 8 red marbles, 5 white marbles, and 7 blue marbles. Randomly choose…

A: Total marbles=8+5+7=20Red marbles=8, White marbles=5, Blue marbles=7

Q: Questi The probability of a type I error is represented by which of the following symbols? O b Ock a

A: The probability of a type 1 error is represents the symbol is (ᾶ) which is greel letter.

Q: Find the mean of the probability distribution.

Q: There are 5 boxes. Box n, where n=1....5, contains n+6 balls. One of the balls in boxes 3, 4 and 5…

Q: Selecting Marbles A bag contains 5 red marbles, 6 white marbles, and 9 blue marbles. Randomly choose…

A: 5 red marbles6 white marbles9 blue marbles

Q: Find (A u B) o B'.

A: Here use basic of venn diagram

Q: Two construction contracts are to be randomly assigned to one or more of three firms: I, II and III.…

A: Getting one contract is independent of getting another contract. As well as the probability that…

Q: Selecting Marbles A bag contains / red marbles, 9 white marbles, and & blue Eime, and without…

Q: Probability of an event are given, compute the probability of the event (enter the probability as a…

A: The probability of an event are given, The probability of the event 2 to 7 = 2/(2+7)

Q: A bag contains 7 red marbles, 5 white marbles, and 8 blue marbles. Randomly choose two marbles, one…

A: From the provided information,A bag contains 7 red marbles, 5 white marbles, and 8 blue…

Q: 2.74 A class in advanced physics is composed of 10 juniors, 30 seniors, and 10 graduate students.…

A: Juniors = 10 Seniors = 30 Graduate students = 10 Total = 50 P(Junior) = 10/50 = 0.2 P(Senior) =…

Q: The addition rule of probability is P(A U B) = P(A) + P(B) – P(A n B). True O False

A: We have to determine the given statement is true or false.

Question

probability 1

(i) Four independent flips of a fair coin are made. Let X denote the number of heads obtained.
Plot the probability mass function of the random variable X – 2.
(ii) Calculate Var (X), if X represents the outcome when a fair die is rolled. Hint: E[X] = 7/2.
(iii) Suppose that the distribution function of X is given by
0,6 <0
b/4, 0≤b<1
F(b) 1/2+ [(b-1)/4], 1≤ b < 2
11/12, 2<b<3
1, 3≤b
=
(a) Find P{X = i}, i = 1,2,3. (b) Find P{1 < X < 3}.
(iv) On a multiple-choice exam with 3 possible answers for each of the 5 questions, what is the
probability that a student will get 4 or more correct answers just by guessing?

Video Video

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1: Introduction:

VIEW

Step 2: Calculation for the required probabilities:

VIEW

Step 3: Construction for the graph of obtained pmf:

VIEW

Solution

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 4 steps with 13 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

Find the odds that a card dealt from a full deck (no jokers) is not an eight. __________ : __________
Pls help with highlighted question
States Infection Recovery A 5677 1276 B 716 10 C 695 303 Based on the result, find the probability that the selected person is: from state B or he is recovered. recovered given that he is from state C.
Only answer D and E The probability is 0.4 that the final exam is difficult. If the final exam is difficult, the probability is 0.3 that Nancy will pass the course. If the final exam is not difficult, the probability is 0.9 that Nancy will pass the course. (A) What is the probability that the final exam is not difficult? (B) What is the probability that the final exam is difficult AND Nancy will pass the course? [Use the multiplication rule.] (C) What is the probability that the final exam is not difficult AND Nancy will pass the course? [Use the multiplication rule.] D) What is the probability that Nancy will pass the course? [Use additivity from (B) and (C).] (E) Given the observation that Nancy passed the course, what is the probability that the final exam was difficult? [Use Bayes’ Theorem.]
Probability & Statistics for it
theoretical probability formula to solve the problem. Express the probability as a fraction reduced to Fri Dec A single die is rolled twice. The set of 36 equally likely outcomes is {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (4, 1), (4,2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 1), (5,2), (5, 3), (5, 4), (5, 5), (5, 6), (6, 1), (6, 2), (6, 3), (6,4), (6, 5), (6, 6)). Find the probability of getting two numbers whose sum is less than 13. A) 2/2 C) 0 D) 1 B) ¹ 4 ical probability formula to solve the exercise. Express the answer as a fraction a decimal, rounded to the nearest thousandth, if necessary. 99 the stock market took big swings up and down. A survey of 1,015 adult in portfolio. The table shows the investor responses. daily?
Probability and Statistics for IT
ASAP