Problem 6: The cumulative distribution function of a random variable X is- {m.x < -1|(x + 1)?, -1< x <1x > 1.0,Fx(x)=1,(a) What is P[X > 0.5]?(b) What is P[-0.5 < X < 0.75]?(c) What is P[|X|< 0.25]?(d) What is the value of a such that P[X < a] = 0.5?

Note: Hey there! Thank you for the question. As you have posted multiple sub-parts, we have solved…

Problem 6: The cumulative distribution function of a random variable X is 0, { {(r + 1)², -1 1. I< -1 Fx(x) = %3D 1, (a) What is P[X >0.5]? (b) What is P[-0.5 < X < 0.75]? (c) What is P[|X|< 0.25]? (d) What is the value of a such that P[X

Problem 6: The cumulative distribution function of a random variable X is 0, { {(r + 1)², -1 1. I< -1 Fx(x) = %3D 1, (a) What is P[X >0.5]? (b) What is P[-0.5 < X < 0.75]? (c) What is P[|X|< 0.25]? (d) What is the value of a such that P[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: Problem 3.1: Suppose the discrete random variable X has the probability distribution listed in the…

A: Given data is x 4 5 6 7 8 9 12 f(x) 0.15 0.20 0.16 0.27 c 0.09 0.03

Q: Problem 3: Let {~ Pois(A) (a random variable with Poisson distribution with rate X). For some natura…

A: Given that ξ~Pois(λ) λ=3 and k=4 Consider, Eξk=Eξ4 =Eξ!4!(ξ-4)!…

Q: Problem 2: X is a continuous-valued random variable with expected value "x = 5 and Var[X] = 3. (a)…

A: A random variable is said to follow uniform distribution if its probability density function is…

Q: (9a+2)(9a+a+) atl

A: Since you have posted multiple questions, as per our policy we will answer first question. Please…

Q: Problem 3. Suppose that X and Y are independent Poisson random variables with param- eters and μ,…

Q: Problem 2.7: The joint probability distribution of the continuous random variables X and Y is…

Q: Problem 2: In problem 1, the following probabilities have been calculated: P(X=1/8) = 0.2, P(X=1/4)…

A: The orders from n=100 customers for wooden panels of various thickness (X) are summarized as:…

Q: • Problem 5: Suppose the random variable X takes the values 0,1,2,.with probability mass function:…

A: Given,P(X)=e-λλxx! ; x≥0

Q: Problem 4: Find EƐ if & have the following distribution function: 0, r 2

A: Given: The cumulative distribution function for ξ is given as:…

Q: Problem 1 Let X1, X2, X3, .., X, be a random sample from an exponential distribution with parameter…

Q: Problem 7: Let X be a continuous random variable with the probability density f(x) = 3x2 for values…

Q: Question 1 Suppose the following expression is given: P(X5-31X4-3,X3-4,X2=1,X1-3, X0-1). Write down…

A: Given the expression : PX5=3/X4=3, X3=4, X2=1, X1=3, X0=1

Q: Problem 3: The joint probability distribution of the discrete variables X and Y is expressed in the…

Q: Problem 1) The cumulative distribution function of the continuous random variable X is: 0. x ½). b)…

A: Solution: Note: Hello! As you have posted more than 3 sub parts, we are answering the first 3…

Q: Problem 10 ) Suppose that battery failure time measured in hours has a probability density function…

A: Answer: 10- Given probability density function f(x) = 2(x+1)3…

Q: Problem 2: Let X,, X2, ...,X, be a collection of independent random variables that all have the same…

Q: Problem 1. Suppose that a temperature X (°C) of an object is a random variable with the pdf f(x) =…

Q: Problem 2 Let the two random variables X and Y be independent, with the following Cumulative…

Q: Problem 1: The following three figures show simulated sample paths of stochastic processes: s00 3…

A: As due to the honor-code, we are authorized to answer only 1 question and that you haven't…

Q: 8

Q: . Herpes simplex-2. Suppose 7.5% of a population is infected with Herpes simplex-2 virus (HSV2). You…

A: Given : Probability(p) = 0.075sample size (n) = 7 X follows Binomial distribution.

Q: Problem 49.19 If the moment generating function for the random variable X is Mx(t) = ,. find E[(X-…

Q: Problem 4 Random variables X and Y are independent, normally distributed, with unit mean and…

Q: Problem 2.11 A random sample X,....,X+1 is taken from a distribution with PDF f. Let Y,..., Y2+1 be…

Q: Problem #1: Consider a population of moose that grows according to P1+1 = Pt + I, where I, = 28 with…

A: Given the population of moose that grows according to pt+1=pt+?t where ?t=28 with a 39% chance…

Q: Problem 2: If x1 is a value from a random sample from a population having a uniform density with a =…

A: The probability distribution function can be written as follows:

Q: Problem 5. A system suffers faults by a Poisson process with rate X. Each fault will, independently,…

A: Given Information: Consider a system that suffers faults which is Poisson distributed with rate λ.…

Q: Problem 5-32. The joint probability distribution of two randoni variables X and Y is given by : P (X…

Q: Problem 7. Suppose X is a continuous random variable with range range(X) = R, whose density fx is…

Q: Problem III Verify that the following function is cumulative distribution function, and determine…

A: given that

Q: The National Institute of Mental Health published an article stating that in any one-year period,…

A: According to the given information in this question We need to apply z test for one population…

Q: Problem 2. Let X be a random variable with probability density |c(4x – 2x²), f(x) = |0, 0 < x < 2…

Q: Problem 2. Let X be a random variable with probability density [c(4x – 2x²), f(x) = |0, 0 < x < 2…

A: we have given that probability density function of x

Q: Problem 2. (a) Consider a random variable X E {1,2,...,n}. Show that (i) µ(X) >0 (ii) o(X) > 0 for…

Q: Problem 5 Let X1, X2, ...,Xn be a random sample from a distribution with pdf T“ for r € (0, µ) |0…

Q: Problem # 4 Let the random variable X has a Poisson distribution with parameter ) Usa Chehyebev's…

Q: Problem 3 Let X1, X2, X3, Xn be a random sample from a Uniform(0,0) distribution, where 0 i- 1...…

Q: Problem 3: Let X be the discrete random variable with the following probability mass function: x…

A: From the given information we find the cumulative distribution function F(2).

Q: Problem 7 Let X1, X2, .., X100 be a random sample from a uniform distribution on the interval (0,1).…

A: Note: Since you have posted a question with many sub-parts, we will solve three sub-parts for you.…

Q: Question 10 In this question we explore the application of MAP and LMS estimation in a communication…

Q: Problem 5 Let X₁,..., X₁ be a sequence of independent, identical distributed random variables, with…

A: X1, X2, ..., Xn is a sequence of independent, identical distributed random variables with mean µ and…

Q: Problem 1. Let x be the level of precaution, w=16 is the marginal cost of precaution, p(x)=1/x is…

Q: Question 7: Let X be a random variable such that E(X- 2)2 = 10 and E(X + 1)² = 4, then a. E(X) = -;…

A: Procedure 1. Break both expression 2. Apply the expectation 3. We get two equation from the…

Q: Problem #4: The cumulative distribution function of a random variable X describing the contamination…

Q: Question 12. Suppose that X has a Poisson distribution. If P(X = 1) 0.5P(X = 0), then E(X) is equal…

Q: . Rework problem 27 from section 4.1 of your text involving a poll of registered voters. Assume that…

Q: Question 1: The cumulative distribution function of a continuous random variable X is given by (0, x…

Q: Problem 1; #11.1: If is a value of a random variable having an exponential distribution, find k so…

A: Introduction:Denote the exponentially distributed random variable as X with parameter θ, of which, x…

Q: Problem 3 Let X be a continuous random variable with values exponentially distributed over [0, 0)…

Q: Problem 4 A confidence interval for uniform distributions Let X1,..., X, be i.i.d. uniform random…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Concept explainers

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!

Question

Problem 6: The cumulative distribution function of a random variable X is
- {m.
x < -1
|(x + 1)?, -1< x <1
x > 1.
0,
Fx(x)
=
1,
(a) What is P[X > 0.5]?
(b) What is P[-0.5 < X < 0.75]?
(c) What is P[|X|< 0.25]?
(d) What is the value of a such that P[X < a] = 0.5?

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

Step 3

Step 4

Trending now

This is a popular solution!

Step by step

Solved in 4 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Continuous Probability Distribution$

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

Find the cumulative distribution function of the random variable X representing the number of defectives in Problem #5. Then using F(x), find (a) P(X = 1); (b) P(0 < X ≤ 2).
Problem 3: Let X be the discrete random variable with the following probability mass function: x 0 1 2 3 f (x) 0.5 0.3 0.1 0.1 Find the value of the cumulative distribution function F(2).
Problem 15-27 (Algorithmic) Gubser Welding, Inc., operates a welding service for construction and automotive repair jobs. Assume that the arrival of jobs at the company's office can be described by a Poisson probability distribution with an arrival rate of three jobs per 8-hour day. The time required to complete the jobs follows a normal probability distribution, with a mean time of 1.9 hours and a standard deviation of 1 hour. Answer the following questions, assuming that Gubser uses one welder to complete all jobs: What is the mean arrival rate in jobs per hour? If required, round your answer to two decimal places.________________per Hour What is the mean service rate in jobs per hour? If required, round your answer to four decimal places.________________per hour What is the average number of jobs waiting for service? If required, round your answer to three decimal places.______________________ What is the average time a job waits before the welder can begin working on it? If…
Problem 14: Suppose that the checkout time at a grocery store is an exponential random variable with mean 4 minutes. Estimate the probability that a cheker will serve more than 77 customers during a 6 hour shift.
Question 23: The National Institute of Mental Health published an article stating that in any one-year period, approximately 9% of American adults suffer from depression or a depressive illness. Suppose that in a survey of 2000 people in a certain city, 10% of them suffered from depression or a depressive illness. Conduct a hypothesis test to determine if the true proportion of people in that city suffering from depression or a depressive illness is more than the 9% in the general adult American population. Test the relevant hypotheses using a 10% level of significance. Give answer to at least 4 decimal places. What are the correct hypotheses? (Select the correct symbols and use decimal values not percentages.) H0: H1: Based on the hypotheses, find the following: Test Statistic = p-value = Based on the above we choose to The correct summary would be: that the true proportion of people in that city suffering from depression or a…
Rework problem 27 from section 4.1 of your text involving a poll of registered voters. Assume that 40 percent of voters are Republicans, 30 percent are Democrats, and 30 percent are Independents. A poll taker asks 9 people at random for their party affiliation. Assume further that, because the city is so large, this situation can be approximated by a Bernoulli process. What is the probability that at least 6 of those polled are Democrat voters?
Question 1: The incomes of all families in a particular suburb can be represented by a continuous random variable. It is known that the median income for all families in this suburb is $60,000 and that 35% of all families in the suburb have incomes above $72,000. a.For a randomly chosen family, what is the probability that its income will be between $60,000 and $72,000? b.Given no further information, what can be said about the probability that a randomly chosen family has an income below $65,000? Question 2: An author receives a contract from a publisher, according to which she is to be paid a fixed sum of $10,000 plus $1,50 for each copy of her book sold. Her uncertainty about total sales of the book can be represented by a random variable with a mean of 30,000 and a standard deviation of 8,500. Find the mean and standard deviation of the total payments she will receive.
Problem 1Let X be a discrete random variable with the following PMF.
Rework problem 27 from section 4.1 of your text involving a poll of registered voters. Assume that 45 percent of voters are Republicans, 35 percent are Democrats, and 20 percent are Independents. A poll taker asks 8 people at random for their party affiliation. Assume further that, because the city is so large, this situation can be approximated by a Bernoulli process. What is the probability that at least 6 of those polled are Democratic voters?
QUESTION 3 H Profits for a skiing resort depends on how much snow falls in winter. The probability distribution of snowfall and resulting profitability is as follows: More than 40 inches K120 000 40% 20 to 40 inches K40 000 20% Less than 20 inches -K40 000 40% The owner receives an offer from a hotel chain to lease the resort at a guaranteed profit of K45 000 for the season. He is also considering leasing snow making equipment which would allow the resort to operate full-time regardless of the amount of natural snow fall which would ensure profit of K120 000 minus the cost of leasing and operating the snow equipment. The leasing cost is K12 000 per season regardless of usage. Operating cost will be K10 000 for natural snowfall of more than 40 inches, K50 000 for between 20 and 40 inches and K90 000 if it is less than 20 inches. Required: Construct a decision tree…
Question 4 (Part B a-c)A petrol station in the capital Kingstown has a single pump manned by one attendant. Vehicles arrive at the rate of 20 customers per hour and petrol filling takes 2 minutes on an average. Assume the arrival rate is Poisson probability distribution and service rate is exponentially distributed. Arrivals tend to follow a Poisson distribution, and service times tend to be exponential. The attendant is paid $10 per hour, but because of lost goodwill and sales, station loses about $15 per hour of customer time spent waiting for the attendant to service and order. The Petrol station is considering adding a second pump with an attendant to service customers. The station would pay that person the same $10 per hour. What is the probability that no customers are in the system (Po)?b. What is the average number of customers waiting for service (Lq)?c. What is the average number of customers in the system (L)? SHOW ALL WORKINGS
Question 15 Suppose you have the following partial information about the cdf (cumulative distribution function) of a random variable X, which takes one of 4 possible values: