Consider a random experiment of throwing three perfectly balanced and identical coins. Suppose that for each toss that comes up heads we win $3, but for each toss that comes up tails we lose $4. Clearly, a quantity of interest in this situation is our total wining. Let X denote this quantity. (n) What are the vilues that the random variable X takes? (b) Find P(X = 9). (e) Find P(X =-5).

Consider a random experiment of throwing three perfectly balanced and identical coins. Suppose that for each toss that comes up heads we win $3, but for each toss that comes up tails we lose $4. Clearly, a quantity of interest in this situation is our total wining. Let X denote this quantity. (n) What are the vilues that the random variable X takes? (b) Find P(X = 9). (e) Find P(X =-5).

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: Suppose you are flipping a coin until you get your first heads. The coin flips are independent, and…

A: A coin is flipped until the first head is obtained.The probability of head is 0.727.

Q: d. Create a probability distribution of X. 1 4 P(X = x) NOTE: 0 < P(x;) < 1 and P(x1) + P(x2) +…

A: X denotes the number of tails that occur. There are total 16 possible outcomes. From the part(a).…

Q: Calculate the probabilities P (X=x) of the probability distribution of X. First, fill in the first…

A: An ordinary (fair) coin is tossed 3 times. outcomes are thus triples of "heads" (h) and "tails" (t)…

Q: Suppose that in a casino game the payout is a random variable X. If X is positive, you gain money,…

Q: In large corporations, an "intimidator" is an employee who tries to stop communication, sometimes…

A: State the hypotheses. That is, there is no evidence to conclude that population mean time lost due…

Q: An ordinary (fair) coin is tossed 3 times. Outcomes are thus triples of "heads" (h) and "tails" ()…

A: The question is about probability distribution Given : To find : Prob. P ( X = x ) of the prob.…

Q: For each outcome, let IV be the random variable counting the number of tails in each outcome. For…

A: The values of X are given in the table belowOutcome thhtthhhhhthttthtthhtthtValue of…

Q: These questions concerns the following situation. There is a rain on a football ground. The ground…

A: Joint Cumulative Distribution Function: The joint cumulative distribution function of two discrete…

Q: Suppose we have a binomial experiment in which success is defined to be a particular quality or…

A: It is given that n is 41 and p is 0.33.

Q: Suppose that X, Y, and Z are jointly distributed random variables, that is, they are defined on the…

A: Given that, E(X) =-9 , E(Y) =-5, E(Z) =-1 Var(X) =3, Var(Y) =1, Var(Z) =34

Q: Define the rejection region as {y : ı – 2 < ci} where c is some real value. a) Calculate the Type I…

A: Here, the null hypothesis is that the recovery time of the participants who are treated with either…

Q: (iii) Given that the events A and B are such that : 3 P(A) = P(AUB)= and P (B) = p. 2' Find the…

Q: Calculate the probabilities P(X=x) of the probability distribution of X. First, fill in the first…

Q: These questions concerns the following situation. There is a rain on a football ground. The ground…

A: Given X is the x-coordinate where a raindrop falls, Y is the y-coordinate of where a raindrop…

Q: For two independent events A and B, if P(A n B) = 0.049 and P(A) = 10P(B), then P(A) is equal to:

A: Step 1:Given that :P(A∩B)=0.049P(A)=10P(B)Find the P(A).Step 2:A and B are independent events.We can…

Q: Suppose the random variable X is unifo Compute answers to two decimal places.

A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts. In case…

Q: Question 6: Circle correct answer choice(s). (i) Let W, X and Y are random variables. Choose the…

Q: An ordinary (fair) coin is tossed 3 times. Outcomes are thus triples of "heads" (h) and "tails" (t)…

A: Given that,N be the random variable counting the number of tails in each outcome.Outcomes for x…

Q: Suppose X and Y are events in a sample space such that P(X|Y) = 1 3 and P(Y) = What is P(XY)?

A: X and Y are the events in a sample space such that, P(X|Y)=1/3 P(Y)=1/5 To find: P(X and Y)

Q: Two teams participated in 4 football game in 2008. The probability distribution for the data…

Q: An ordinary (fair) coin is tossed 3 times. Outcomes are thus triples of “heads” (h) and “tails” (t)…

A: In this case, the random variable R defines the number of heads.

Q: An ordinary (fair) coin is tossed 3 times. Outcomes are thus triples of "heads" (h) and "tails" (t)…

A: It is given that an ordinary coin is tossed 3 times.

Q: (b) Find a 90% confidence interval for - 2. (Round your answers to two decimal places.) lower limit…

A: Confidence Interval: In statistics, we can say a range of values of the specified population…

Q: Calculate the probabilities P (X = x) of the probability distribution of X. First, fill in the first…

A: Given that An ordinary (fair) coin is tossed 3 times Outcomes = (ttt , tth , tht , htt , hht , hth…

Concept explainers

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

Consider a random experiment of throwing three perfectly balanced
and identical coins. Suppose that for each toss that comes up heads we win $3, but for each
toss that comes up tails we lose $4. Clearly, a quantity of interest in this situation is our
total wining. Let X denote this quantity.
(a) What are the values that the random variable X takes?
(b) Find P(X = 9).
(c) Find P(X = -5).
(d) Find P(X = 2).
(e) Find P(X = -12).
(f) Find P(X = 3).
(g) Find P(X =-1).

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

Step 2-a

Step 3-b

Step 4-c

Trending now

This is a popular solution!

Step by step

Solved in 4 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Point Estimation, Limit Theorems, Approximations, and Bounds$

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

In large corporations, an "intimidator" is an employee who tries to stop communication, sometimes sabotages others, and, above all, likes to listen to him or herself talk. Let x1 be a random variable representing productive hours per week lost by peer employees of an intimidator. x1: 7 4 7 2 2 5 2 A "stressor" is an employee with a hot temper that leads to unproductive tantrums in corporate society. Let x2 be a random variable representing productive hours per week lost by peer employees of a stressor. x2: 3 3 10 7 6 2 5 8 (i) Use a calculator with sample mean and sample standard deviation keys to calculate x1, s1, x2, and s2. (Round your answers to two decimal places.) x1 = s1 = x2 = s2 = (ii) Assuming the variables x1 and x2 are independent, do the data indicate that the population mean time lost due to stressors is greater than the population mean time lost due to intimidators? Use a 5% level of significance. (Assume the population distributions of time…
I need the answer as soon as possible
An ordinary (fair) coin is tossed 3 times. Outcomes are thus triples of "heads" (h) and "tails" (1) which we write hth, ttt, etc. For each outcome, let N be the random variable counting the number of heads in each outcome. For example, if the outcome is htt, then N (htt) = 1. Suppose that the random variable X is defined in terms of N as follows: X=2N-N2 -4, The values of X are given in the table below. Outcome hht tth hth thh tht ttt hhh htt Value of x -4 -3 -4 -4 -3 -4 -7 -3 Calculate the probabilities P(X=*) of the probability distribution of X. First, fill in the first row with the values of X. Then fill in the appropriate probabilities in the second row. Value of x _ _ _ p(X=x) _ _ _
An ordinary (fair) coin is tossed 3 times. Outcomes are thus triples of "heads" (h) and "tails" (t) which we write hth, ttt, etc. For each outcome, let R be the random variable counting the number of heads in each outcome. For example, if the outcome is hth, then =Rhth2. Suppose that the random variable X is defined in terms of R as follows: =X−2R1. The values of X are given in the table below. Outcome tth thh hht htt ttt hhh hth tht Value of X 1 3 3 1 −1 5 3 1 Calculate the values of the probability distribution function of X, i.e. the function pX. First, fill in the first row with the values of X. Then fill in the appropriate probabilities in the second row. Value x of X pXx
Suppose that X, Y, and Z are jointly distributed random variables, that is, they are defined on the same sample space. Suppose that we also have the following. E(X)=-6 E(Y)=-9 E(Z)=3 Var (X)=8 Var (Y)=14 Var (Z)=25 Compute the values of the expressions below. E (-1- 37) - I -2x - 5z 4 Var (47) - 2 - I e(32°) - [I Dlo
An ordinary (fair) coin is tossed 3 times. Outcomes are thus triples of "heads" (h) and "tails" (t) which we write hth, ttt, etc. For each outcome, let N be the random variable counting the number of tails in each outcome. For example, if the outcome is hth, then N (hth) = 1. Suppose that the random variable X is defined in terms of N as follows: X=2N² -6N-1. The values of Xare given in the table below. Outcome thh tth hhh hth ttt htt hht tht Value of X -5 -5 − 1 -5 −1 -5 -5 -5 Calculate the probabilities P(X=x) of the probability distribution of X. First, fill in the first row with the values of X. Then fill in the appropriate probabilities in the second row. Value X of X P(X=x) 0 8 X
Consider the following random experiment: we toss a two-sided coin (H on one side and T on the other side) n = 3616 times. In any given toss, the probability the coin comes up H is p = P(H) = 0.3. Each time the coin comes up H we give Tom 2 dollars and each time the coin comes up T we take from Tom 1 dollar (so Tom either gets 2 or gets -1, i.e., loses 1 dollar). How many dollars do we expect Tom will get on "average", i.e., per experiment?
Consider the following game. A fair coin is flipped until the first tail appears; we win $2 if it appears on the first toss, $4 if it appears on the second toss, and in general if it first occurs on the k-th toss. Let the random variable X denote our winning. How much should we have to pay in order for this to be a fair game? Note: A fair game is one where the difference between the ante and E(X) is 0
These questions concerns the following situation. There is a rain on a football ground. The ground is 100 meters long and 70 meters wide. Model the event of a raindrop falling as a randomly selected point in the rectangle pictured.Lets imagine the following random variables: X is the x-coordinate where a raindrop falls, Y is the y-coordinate of where a raindrop falls, and Z=X+Y. CHOOSE ONE AND SHOW THE PROCESS. Which one of the following statements are true? * a) X and Y are independent b) X and Z are independent c) Y and Z are independent
An ordinary (fair) coin is tossed 3 times. Outcomes are thus triples of "heads" (h) and "tails" (t) which we write hth, ttt, etc. For each outcome, let N be the random variable counting the number of heads in each outcome. For example, if the outcome is thh, then N (thh)=2. Suppose that the random variable X is defined in terms of N as follows: X=2N²-6N-4. The values of X are given in the table below. ttt hhh hth hht tht htt thh tth Value of X -4 -4 -8-8-8-8-8-8 Outcome Calculate the probabilities P (X=x) of the probability distribution of X. First, fill in the first row with the values of X. Then fill in the appropriate probabilities in the second row. Value x of X P(X=x) 7 00 X S
An ordinary (fair) coin is tossed 3 times. Outcomes are thus triples of "heads" (h) and "tails" (t) which we write hth, ttt, etc. For each outcome, let N be the random variable counting the number of heads in each outcome. For example, if the outcome is hhh, then N (hhh) = = 3. Suppose that the random variable X is defined in terms of N as follows: X=6N-2N²-3. The values of X are given in the table below. Outcome hhh hth hht thh htt tth ttt tht Value of X-3 1 1 1 1 1 -3 1 Calculate the probabilities P (X=x) of the probability distribution of X. First, fill in the first row with the values of X. Then fill in the appropriate probabilities in the second row. Value X of X P(X=x) 0 0 0 00 X
Two coins are taken at random (without replacement) from a bag containing 4 nickels, 5 dimes, and 8 quarters. Let X denote the random variable given by the total value of the two coins. Find E(X). (Round your answer to four decimal places.)E(X) = $