a) Let probability that a child will be born with black eyes is 1/3, determinethe probability that only the fifth child of a family will be born with blackeyes, and find its E(X), Var(X).

It is given the probability that a child will be born with black eyes is 1/3 i.e. p=1/3. It has been…

Answered: Let probability that a child will be…

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

Similar questions

Suppose we roll 2 six-sided dice. Let X be their sum and Y be the larger value of the two. (a) (10 points) What is E[X]? (b) (10 points) What is E[Y]?
Assume that there is a rare disease. It occurs in the population at a rate of 1 per 1000; that is, P[disease] = 0.001. There is a test for the disease that has an error rate of 5% for in positive and negative senses. That is, if a patient has the disease, there is 95% probability that the test will confirm that status and 5% probability that the test will be negative. Conversely, if the patient does not have the disease, there is 5% probability that the test will indicate erroneously that the disease is present and 95% probability that the test will confirm that the disease is not present. Let PT indicate a positive test, D indicate the disease is present, and a bar over a symbol indicates the negative, so this can all be summarized as Po(D) = 0.001 P(PT|D) = 0.95 P(PT|D) = 0.95 P(PT|D) = 0.05 P(PT|D) = 0.05 The disease is serious, and the treatment is difficult and expensive, so a decision either to treat or not to treat the disease is not trivial. A patient takes the test and…
Suppose a basketball player who makes a free throw shot with success 80%. Let X be the number of the successful shots among n = 5 shots. (a) What is the probability that a basketball player makes exactly 4 shots successfully, or, P (X = 4)? (b) W h a t i s P (X = 5)? (c) Calculate P (X < 4), that is, the probability that this player makes less than 4 successful shots.
gn X Three couples and two single individuals have been invited to an investment seminar and have agreed to attend. Suppose the probability that any particular couple or individual arrives late is 0.41 (a couple will travel together in the same vehicle, so either both people will be on time or else both will arrive late). Assume that different couples and individuals are on time or late independently of one another. Let X = the number of people who arrive late for the seminar. (a) Determine the probability mass function of X. [Hint: label the three couples #1, #2, and #3 and the two individuals #4 and #5.] (Round your answers to four decimal places.) P(X = X) X 0 1 2 3 4 5 6 7 8 (b) Obtain the cumulative distribution function of X. (Round your answers to four decimal places.) F(x) X 0 1 2 3 4 5 6 7 Use the cumulative distribution function of X to calculate P(2 ≤ x ≤ 5). (Round your answer to four decimal places.) P(2 ≤ x ≤ 5) = Need Help? Read It Watch It 4
Suppose that you start with an initial fortune of 20 dollars, and you bet one dollar each time. The probability of winning each hand is p. You quit if you reach your goal of L dollars or when you go broke. Let Q(xo) denote that probability that you eventually win. We need to characterize this probability. Next we give a more mathematical description of the problem. Now define your fortune at time n ≥ 1 by - Xn = Xn-1+ I{Y=1} = I{Yn=0} with the initial condition X = x0 ≥0. Let L = N be given, and define T inf{k : Xk = 0 or Xk = L}. Finally, let Q(x0) = P{XT = . L}. Show that X is a Markov chain and obtain its transition probability matrix. Is it irreducible? Use conditional expectations to prove that Q(x)=pQ(x+1) + (1 − p)Q(x − 1), - x = 1, L-1, (1) with Q(0) 0 and Q(L) = 1. = d) Solve the difference equation in (1) analytically. Let P(x0) P{XT = 0}. Determine P(x) directly and show that P(x) + Q(x) = 1. Hint: Use the same form of the difference equation and analytical solution as in…
Let the probability function of the random variable X bef(x) = { x/45 if x = 1, 2, 3, ⋯ ⋯ ,9 { 0 otherwiseFind E(X) and Var(X)
Suppose that the length of time spent by a student with a professor during office hours in minutes is an exponential r.v. with parameter ?=1/10. This professor only sees students in the office hour one at a time. Thus, if you arrive to the office and there is someone inside, you have to wait. Consider 5 randomly chosen days in which you visit the professor's office during the office hour period and someone arrives immediately ahead of you. What is the probability that in one of those days you will have to wait between 10 and 20 minutes?
The time (in hour) to failure of a component after starting a new machine is exponentially distributed with mean 3 hours. If 2 hours have passed with no component failure after starting the machine, what is the probability that the component will fail in the next hour? Choose the correct equation to aswer the question. Оа. Р(X 2) — Р(X 3|X 3|X > 2) = P(X > 1)
Help me please
If the odds against R occurring are 1:7, then find P(R) and P(R'). P(R)= (Simplify your answer.) P(R')= (Simplify your answer.)
Assume that the entire sample has 8 positive observations and 4 negatives observations. Variable X1: at the left branch has 9 positive observations and 3 negatives observations;at the right branch has 8 positive observations and 8 negative observations. What is the information gain or reduction in uncertainty of X1 using the Gini index? (round to two decimal spaces)
When a man observed a sobriety checkpoint conducted by a police department, he saw 656 drivers were screened and 5 were arrested for driving while intoxicated. Based on those results, we can estimate that P(W)equals=0.00762,where W denotes the event of screening a driver and getting someone who is intoxicated. What does P(W) denote, and what is its value? What does P(W) represent? P(W)=

SEE MORE QUESTIONS

Recommended textbooks for you

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

SEE MORE TEXTBOOKS

Let probability that a child will be born with black eyes is 1/3, determine the probability that only the fifth child of a family will be born with black eyes, and find its E(X), Var(X).