probability 2 (i) Find Var(X), if the density function of X isf(x) =2x, 0 ≤ x ≤ 10, otherwise.(ii) A system consisting of one original unit plus a spare can function for a random amount oftime X. If the density of X is given (in units of months) byCa[Cxe-x/², x>010, x ≤0what is the probability that the system functions for at least 4 months?f(x) =(iii) Suppose that X is a normal random variable with mean 5. If P{X > 9} = .2, approximatelywhat is Var (X)?

X is a random variable of the system functions

(ii) A system consisting of one original unit plus a spare can function for a random amount of time X. If the density of X is given (in units of months) by [Cxe-x/2, x>0 10, x ≤0 what is the probability that the system functions for at least 4 months? f(x) = =

(ii) A system consisting of one original unit plus a spare can function for a random amount of time X. If the density of X is given (in units of months) by [Cxe-x/2, x>0 10, x ≤0 what is the probability that the system functions for at least 4 months? f(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: Suppose we have a bowl with 10 marbles - 2 red marbles, 3 green marbles, and 5 blue marbles. We…

A: Answer - We have a bowl with 10 marbles- 2 red, 3 green, and 5 blue marbles We…

Q: 22) A blood test is used to determine whether a person has a disease. 1% of the total population has…

A: Let D be the event that a person has the disease, and let P be the event that the blood test outcome…

Q: 16 The probability that an event will happen is P(E) = 19 Find the probability that the event will…

A: Given The probability that an event happen is P(E)=1619 Result: For any event A is a subset of…

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: Example There are 3 red balls and 4 blue balls in a box. Two draws are taken from the box with…

A: Number of red balls = 3Number of blue balls = 4Total balls = 3+4 = 7

Q: nd the probability that the dictionary is select nd the probability that 2 novels and 1 book of |…

A: The formula to compute ncr is, ncr = (n!) /(n- r)! r!

Q: II. Proving Show that P(AB) ≥1-P(A)-P(B), where A, B is any two events.

A: A and B two events are given

Q: A pair of dice is thrown. If it s known that one die shows a 4, what is the probability that (a)…

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: The 30 The probability of event A occurring is. The probability of events A and B occurring is 30°…

Q: Let A and B be two events such that p(A) = 0.4 and P(BA) = 0.2. Then P(BnA) = 0.4 0.7 0.6 0.5

Q: Assuming boys and girls are equally likely, find the probability of a couple having a baby girl when…

A: Given information- We have given that the first four children were all girls. Assuming that boys and…

Q: A buffet has 7 main dishes and 4 desserts. How many different combinations can one choose, if one…

A: Find the number of different combinations can one choose if one takes at least 1 and at most 3 main…

Q: A and B are two events such that P(A) = = 0.4 and P(AB) = 0.2 Then P(An B) is equal to a. 0.4 b. 0.6…

A: Given : P(A) = 0.4 and P(A n B) = 0.2

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: Of the 17-year-old persons who hold a driver's license, 85% have had a driver's ed course, and 15%…

A: And: 0.77

Q: P(B) = 1/3 P(C) = 1/6 Find the probability. (Enter the probability as a fraction.)…

A: Given information- P(B) = 1/3 P(C) = 1/6 We have to find the probability-

Q: Guessing on an exam, In a multiple choice exam, there are 5 questions and 4 choices for each…

A: a) There is total 5 multiple choice questions, where each of the question has 4 choices.

Q: You randomly choose a ball from a bag. The bag contains 3 red balls, 10 green balls, 8 blue balls…

A: We want to find probability of choosing green ball.

Q: The probability that an event will happen is P(E)3= 18 Find the probability that the event will not…

A: Event: In probability theory, an event is an outcome or a set of outcomes of a random experiment to…

Q: Two cards are drawn without replacement from an ordinary deck. Find the probability that two queens…

Q: Suppose you flip 50 fair coins. (a) How many possible outcomes (microstates) are there? (b) How many…

A: As per our guidelines we are supposed to answer only 3 subparts of any questions so i am solving…

Q: A child flips 3 coins. What is the probability that the child flips 1 or 2 tails (based only on what…

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

Q: $ Correct Answer You Answered F5 | _| 1:2l Two tickets are drawn with replacement from the following…

A: From the provided information,Total box = 95 ticket box = 2Odd number ticket box = 6

Q: and Team3 based on their preliminary round. If the probability of winning the competition by Team1…

Q: 8. P(diamond) 25 b. 375 c. 5 d. 625 e. .75 a. P(red face card) a. 26 3 b. 13 3 C. 52 d. 5000 e. 4275…

A: We have given that a standard deck having 52 cards of four suits namely spade, club, diamond and…

Q: Suppose that a family has 8 children. Also, suppose that the probability of having a girl (based on…

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: 2. A large corporation determines that 20% of its employees leave the company taking up an offer…

Q: 22 Find the probability that the event will not happen. The probability that an event will happen is…

Q: A single marble is picked from the container

A: Given that Container contains Red marbles = 4 White marbles = 3 Yellow marbles = 5 Total marbles…

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: Multiplication rule, says that P(A and B) = P(A) x P(B). What must be true about events A and B…

A: Solution -Multiplication rule, says that P(A and B) = P(A) x P(B). What must be true about events A…

Q: The probability that an event will happen is P(E) =7 13 Find the probability that the event will not…

A: By using the given information,Probability that an event will happen = 1317

Q: Find the probability that the sum is as stated when a pair of dice is rolled. (Enter your answers as…

A: Given data A pair of dice is rolled

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.

Q: Two firms V and W consider bidding on a road-building job, which may or may not be awarded depending…

A: Given V= Firm V get job W= Firm W does bid Wc=Firm W does not bid Firm V submits a bid and the…

Q: You are going to randomly choose 2 poker chips from a bag, one at a time, and record the color of…

A: Given, 6 red chips 3 blue chips 7 yellow chips Total = 16

Question

probability 2

(i) Find Var(X), if the density function of X is
f(x) =
2x, 0 ≤ x ≤ 1
0, otherwise.
(ii) A system consisting of one original unit plus a spare can function for a random amount of
time X. If the density of X is given (in units of months) by
Ca
[Cxe-x/², x>0
10, x ≤0
what is the probability that the system functions for at least 4 months?
f(x) =
(iii) Suppose that X is a normal random variable with mean 5. If P{X > 9} = .2, approximately
what is Var (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.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1: Introduction

VIEW

Step 2: Solution

VIEW

Solution

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

Can you please check my work
Pls help with highlighted question
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
2990 You're a sociologist studying whether grocery prices are different in the inner cities than they are in the suburbs. To investigate this, you pick a random set of items (a basket of goods), and then send shoppers to buy these items at an inner city (IC) grocery, and also at a suburban (SU) grocery. You pick 29 different baskets of goods, so your secret shoppers buy 29 baskets, once at the inner city store, and once at a suburban store. Prices could be higher in the inner city because of discrimination, or they could be higher in the suburbs because of the greater disposable income. Use Excel to test the research hypothesis that inner city prices are different than the suburb's prices. The null hypothesis is that inner city prices are equal to suburban prices. You test at the alpha = 0.10 significance level. What do you conclude? Are prices the same? Who has higher prices? Group of answer choices You reject the null hypothesis; prices are different. Grocery prices are higher in…
#2, Suppose that X and Y have joint density given by: f (x, y) = 15x²y, 0 < x < y < 1. (a) Find the marginal pdf of Y. (b) Find the conditional pdf of X given Y. (c) Find the conditional expectation of X given Y = 1/3. (d) Are X andY independent? Show this in two different ways. (e) Give an integral expression for P(X + 2Y < 1), but do not evaluate it.
Probability and Statistics for IT
ASAP
Solve it correctly please please. I will rate accordingly with 4votes. I need correct answer.
Please urgent