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: Compute the probability of event E if the odds in favor of E are 22 28 (C) 5 29 (A) 9 14 (A) P(E)=…

A: Since you have posted a question with multiple sub parts, we will provide the solution only to the…

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: Ans. 1/243, 10/243, 40/243, 80/243, Q.6 If 20 % of the bolts produced by a machine are defective,…

A: Given : Let X : No. of bolts produced by a machine are defective n=5 p=0.20

Q: Determine the probability as a fraction. (a) P(G) (b) P (G|E) (c) P(G AND E)

A: We have given that 9 card , 4 are green and 5 are yellow 4 green cards are numbered 1,2,3,4 5…

Q: It is given that the two events A and B are such that P(A) =0.5 and P(B) = 0.7. Circle ONLY one of…

A: Two events A and B are said to be mutually exclusive, if P(A and B) = 0

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

A: (a) The total outcome for pair of dice is rolled is 36. The outcome for sum of 8 is {(2 6) (6 2) (3…

Q: a small restaurant offers a dinner menu of four salads six entrées and two desserts what is the…

A: No.of salads = 4 No.of entrées = 6 No.of desserts = 2 Total number of items in a menu = 12 (i.e.…

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: Let A and B be events such that, P(A) = 0.6, P(B) = 0.7, P(A N B) = 0.4 Find %3D %3D a. P(A U B) b.…

A: (a) PA∪B=PA+PB-PA∩B=0.6+0.7-0.4=1.3-0.4=0.9 therefore, PA∪B=0.9 (b) PA|B=PA∩BPB substitute the…

Q: A charity holds a raffe in which each ticket is sold for $100. A total of 10,000 tickets- are sold.…

A: Given data: Total number of tickets sold, N = 10000. Each ticket is sold for x = $100. The raffle…

Q: Leila owns a pizza shop. She determines the number of pizza boxes that are sold per day. Probability…

A: It is given the probability distribution of number of pizza boxes sold per day We need to check if…

Q: Two events (A) and (B) are : independent if P(A U B) = P(A)P(B) O P(An B) = P(A)+P(B) O P(A U B) =…

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

Q: A student is taking a multiple choice quiz but forgot to study and so he will randomly guess the…

A: Since there are 4 possible answer among which one is correct therefore Probability (p) = 1/4 =…

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: 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: (a) Compute the probability of randomly selecting a club or heart. (b) Compute the probability of…

A: The experiment is of a standard deck of cards. Total no. of cards = 52 One card can be selected from…

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: n(E) Use the formula P(E) = n(S) - to find the probability of selecting the following cards from a…

A: It is a Probability problem, so I used the formula of probability and combination to solve the…

Q: A student goes to the library. Let events B = the student checks out a book and D = the student…

A: Given,P(B)=0.33P(D)=0.24P(D|B)=0.52

Q: Find Reliability of electrical circuits shown (All components are independent) P(A)-85% P(B)- 90% A…

A: Given:R(A) = reliability of component A, which is 85 % or 0.85 .R(B) = reliability of component B,…

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: How do you test a hypothesis Formula and example

A: Answer:

Q: In iTech marathon competition, 16 students registered for participation. The students are divided…

A: This question is based in the rule that total probability is always 1.

Q: The time that a machine takes to produce a widget is a continuous uniform random variable ranging…

Q: uppose that you have 7 green cards and 5 yellow cards. The cards are well shuffled. You randomly…

A: We have, N= 7+5 =12 n1= 7 = the number of green cards n2= 5 = the number of yellow cards The two…

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

Q: Find the probability of an event and interpret it

A: I would like probability models to have an interpretation in the real world. Otherwise, what am I…

Q: Show that if 4, and A, are two events, then P(A₂)+P(A₂)−1≤P(44₂).

A: First we will write Inclusion-exclusion principle for two sets.

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: Tom exercises shooting. He is allowed to make 3 shoots. For every shoot Tom makes, Probability of…

A: Given data: The total number of shoots is n=3. The number of shoots exactly hit by Tom is r=2. The…

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…

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

Suppose P(A) Find the probability. 4 P(A)
Interpretation You are applying for two jobs, and you estimate the probabil- ity of getting an offer for the first job is 0.70 while the probability of getting an offer for the second job is 0.80. Assume the job offers are indene
Multiplication rule, says that P(A and B) = P(A) x P(B). What must be true about events A and B play this rule to apply.
The probability that an event will happen is P(E) =7 13 Find the probability that the event will not happen. The probability that the event will not happen is| (Type an integer or a simplified fraction.)
Help please
Events A and B are independent. Find P(B). P(A) = 0.29 P(B|A) = 0.80
Current Attempt in Progress Use the information that, for events A and B, we have P(A)= 0.5, P(B) = 0.2, and P(A and B)= 0.1. Find P(A or B). Enter the exact answer. P(A or B) =
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…
A conditional Probability: P(A | B) is asking what is the probability we get event A if we know that event B occurred. A useful formula: P (A | B) = ||| P(A and B) P(B) Or: P(A | B) = (remaining # of ways to get A) / (remaining number of possible outcomes) A bag has 5 red balls, 7 green balls, and 8 purple balls. Two balls are going to be selected. After the first ball is drawn it is NOT returned to the bag. Find the probability the second is a red ball if you know the first chosen is a red ball. If A = event a red ball is selected: P(A|A) = ?
Pls help ASAP
Please do not give solution in image format thanku (Probability) Suppose that you are a merchant selling diamonds. You have three types of jewelry to sell: costume, average quality, and luxury. Costume jewelry sells for $20 per piece, average quality jewelry for $100 per piece, and luxury jewelry for $1000 per piece. Suppose, based on previous monthly sales, you expect to sell 100 pieces of costume jewelry, 30 pieces of average quality jewelry, and 5 pieces of luxury jewelry. What is expected sales this month from selling jewelry?