Five independent flips of a fair coin are made. Let Y be the number of tails obtained. a) Find the probability distributions of Y and of X = 3Y . b) Calculate and compare E(Y ) and E(X). c) Calculate and compare V (Y ) and V (X)

Five independent flips of a fair coin are made. Let Y be the number of tails obtained. a) Find the probability distributions of Y and of X = 3Y . b) Calculate and compare E(Y ) and E(X). c) Calculate and compare V (Y ) and V (X)

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: . Determine the value c so that each of the following functions can serve as probability…

A: Find the value of constant value (c)

Q: Let X refer to the sum of two rolled die. Describe the probabilities of each outcome. If pX(x) is…

A: It is given that x denotes the sum of two rolled dies.

Q: Let X be a random variable with the probability distribution below. Find Horx), where g(X)= (2X+3)-.…

Q: What is the probability that Randolph stays within the restaurant for at most 18 minutes, i.e.…

Q: a) Find the value of k, b) Form the table of probability distribution of X, c) Find the mean and…

A: here given discrete probability distribution of x p(x) = kx2 for x= 1,2,3,4 here use total…

Q: Determine the value of k so that the function f(x)= k(x² + 4) may be used for x = 0,1,2,3, there is…

A: From the provided information, f(x) = k (x2 + 4) for x = 0, 1, 2, 3 there is a valid probability…

Q: FILE ERS TALS URSES A 0.25 d. Are events A and C mutually exclusive? Yes, they are mutually…

A: solution of the given question is like this;as in the given question; from the part d) and e) we can…

Q: Consider random variables X and Y with x = 0 x = 1 fx,y(x, y) in the table. Find fxy (1|0) and…

A: Let X and Y be represent the random variable having joint probability distribution f(x,y) We have…

Q: You roll a pair of dice. The random variable X is the smaller of the two values, while the random…

A: Given that the pair of dice was thrown then the outcomes will be…

Q: Consider the joint probability distribution below. Complete parts (a) through (c). Y Y 0 1 0 1 Pw…

A: Given that: Joint probability distribution: X 1 2 Y 0 0.30 0.10 1 0.40 0.20

Q: 9. Given that f(x, y) = (2x+2y)/2k if x = 0,1 and y = 1,4, is a joint probability distribution…

Q: Below you will find the joint probability distribution to the random variables X and Y. X - 1 - 2…

Q: I are independent. Eunction of W given L = 2. a formed A = Lx W Find the range

A: *Answer: Since there are multiple questions, according to Bartleby policy we will answer the first 3…

Q: Example . Let the random variable X of the continuous type have the p.d.f. Ax) = 2/x', 1 <x < o,…

Q: X 1 2 Y O 0.70 0.00 1 0.00 0.30 a) Compute and interpret the covariance and correlation between the…

Q: Let the r.v. X assume the value 'r' with the probability law : P(X = r) = q-¹ p ; r = 1, 2, 3. Find…

A: The probability mass function of X is given as-

Q: The common probability function of X and Y random variables like this a. Find the value of Cov (X,…

Q: In a family with three children, find the mean of the number of children who will be girls if the…

Q: Let X and Y be dependent random variables. Which statements are always true? Select one or more:…

A: # Let X and Y be dependent random variables. Which statements are always true?

Q: A motorcycle drives from Morayta to Lacson and back using the same course everyday. There are four…

A: Given: x y 0 1 2 3 4 0 0.01 0.01 0.03 0.07 0.01 1 0.03 0.05 0.08 0.03 0.02 2…

Q: Suppose X and Y have the joint probability distribution given by the table shown below. Compute…

Q: We roll 2 six-sided dice. Let X be their sum and Y be the larger value of the two. Find E[X] and…

Q: Let F(z) be the cumulative distribution function (cdf) of a random variable X. Which of the…

A: Based on the property of cumulative distribution, P(a<X<b) = F(b) - F(a) F(a) + P(a<X<b)…

Q: Let X and Y be discrete random variables with joint probability function: P( x, y ) = ( 2x + y )/12,…

A: Let X and Y be discrete random variables with joint probability function:P( x, y ) = ( 2x + y )/12,…

Q: Let P(Z)=0.51, P(Y)=0.32, and P(Z∪Y)=0.67. Find each probability. (a) P(Z′ ∩ Y′)= (b) P(Z′ ∪…

A: Let P(Z)=0.51, P(Y)=0.32, and P(Z∪Y)=0.67.Find each probability.(a) P(Z′ ∩ Y′)=(b) P(Z′ ∪ Y′)=(c)…

Q: Let X represent the number of tires with low air pressure on a randomly chosen car. a. Which of the…

A: a. Consider a random variable x with probability mass function of p(x). The necessary conditions to…

Q: What values of a, b, c, and d should be used to calculate the probability shown below? xy OSxS1…

Q: Find the variance of probability function 1 2 4 P(X) 0,25 0,15 0,10 0,25 0,25 21 - O A) 6,80 O B)…

A: Here, X P(X) X.P(X) X2 X2.P(X) 0 0.25 0 0 0 1 0.15 0.15 1 0.15 2 0.1 0.2 4 0.4 3 0.25…

Q: Find the probability distribution for Y. The table for the probability distribution of Y may have…

A: Here, Y = X^2 + 1

Q: A discrete random variable Y has probability distribution given in the table below. Y 1 2 3 P(Y=y)…

A: Given : A discrete r.v Y has dist. given in the table Y 1 2 3 Total P(Y=y) 0.6 0.3 0.1 1

Q: Let X and Y be two independent random variables such that E[X]=3, E(Y)=4, V(X)=10 and V(Y)-20. Then…

A: According to the given information, we have E(X)=3E(Y)=4V(X)=10V(Y)=20

Q: Suppose that a pair of fair dice are to be tossed, and let the random variableX denote the sum of…

A: A pair of fair dice to be tossed.The possible outcomes are 62 = 36The sample space is,S={ (1, 1),…

Q: The distributions of X and Y are described below if X and Y are independent, determine the joint…

A: Given that, X01P(X)0.280.72 Y123P(Y)0.430.230.34

Q: The simultaneous probability distribution of the random variables X and Y is given below. X - 2 2 -…

A: Note: According to bartleby experts question answers guidelines an expert can solve only first three…

Q: Please show work. X and Y are two discrete random variables having the joint probability…

A: Cov(X,Y)=E(XY)-E(X)E(Y)corr(X,Y)=Cov(X,Y)V(X)V(Y)

Q: F(x) is cdf of X. Cumulative probability X is 2,4,7 and 9 is 0.1,0.4,0.8 and 1. calculate the…

A: We can right this cdf in tubular form as X 2 4 7 9 F(X) 0.1 0.4 0.8 1 Hence we have…

Q: Find conditions on the numbers a and b such that the table gives the probability distribution of the…

A: To find a + b of the given probability distribution table.

Q: Q: Let X and Y be random variables such that E[X] = 2 and E[Y] = 3 . a. Find E[4X + 5Y] . b. Find…

A: It is given that E(X)=2 and E(Y)=3.

Q: a is normally distributed. The probability that X is between-t and t is 88%. Find the probability…

A: given data normal distribution P(-t<x<t) = 0.88 P(x<t) = ?

Q: Two cards are drawn at random without replacement from an ordinary deck of 52 cards. Let X be the…

A: Given: X = number of hearts Y = number of red cards n (total) = 52 n (hearts) = 13 n (red) = 26…

Question

Five independent flips of a fair coin are made. Let Y be the number of tails obtained.

a) Find the probability distributions of Y and of X = 3Y .

b) Calculate and compare E(Y ) and E(X).

c) Calculate and compare V (Y ) and V (X)

Video Video

Expert Solution

This question has been solved!

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

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step by step

Solved in 4 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Multivariate Distributions and Functions of Random Variables$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.

Similar questions

Let E and F be independent events such that P(E) = 0.4, P(F) = 0.6.. Find P(E| F) and P(E U F). 5.
The marginal distributions of two random variables X and Y, together with some values of their joint distribution, are given in the table below. Fill in the table in such a way that X and Y are dependent random variables. Y=0 Y= 1 Y= 3 X=-1 0.06 0.60 X=3 0.04 0.40 0.50 0.10 0.40 1.00
k is a probability distribution 4* Given that p(x) = for a random variable X that can take on the values x = 0, 1, 2, and 3. k is a constant. a) Find the pmf of X. b) Find the mean of X c) Find the variance of X
statistic discrete rondom variables
The marginal distributions of two random variables X and Y, together with some values of their joint distribution, are given in the table below. Fill in the table in such a way that X and Y are independent random variables. Y= 1 Y= 3 X= 0 0.50 X= 1 0.30 X= 2 0.10 0.10 0.20 0.50 0.50 1.00
Calculate the expected value of X, E(X), for the given probability distribution. E(X) = X P(X = x) 10 15 50 20 10 50 30 20 50 40 5 50
Let X and Y be two random variables. Suppose we know E(X) = 7 and E(Y)=3.Let Z = X − Y be a random variable. What is E(Z)? Justify your answer.
Solve it correctly please. I will rate accordingly.
A probability function for a discrete random variable, Y, is shown below. y P(Y=y) 4 0.4 6 0.2 8 0.2 10 0.2 Show how you would calculate the mean of Y. (You do NOT need to work this out). μ=
Find P(XS3) if the cumulative distribution function for the random variable X is: 0, x<-1, 0.25, -15x<1, F(x)=0.5, 15x<3, 0.75, 35x<5, 1, 5Sx. Select one: a. 0.75 b. 1.0 c. 0.25 d. 0.50
Find E(x) and Var(x) of X, where X is the discrete random variable whose probability table is given below. outcome Probability 1 3 4 7 0.2 0.5 0.1 0.2
Find the marginal probabilities of each random variable X and Y in thefollowing table:- Compute the covariance and the correlation of these two random variables.