II.Analyze and solve the following problems:1. A cloth bag contain numbers 1,2 3, and 4. The following is the probabilitydistribution of the sum when two numbers from each box is taken at a time withreplacement.5.78XP(x)2.341/81/16 1/43/161/163/161/8a. Find P(odd)b. Find P (X2 3)c. Find P(X>8)d. Find the probability of the value between 8 and 4.

Answered: Image /qna-images/answer/dc9ce192-345e-4959-b60b-75b37f3b88a4.jpg

Answered: 1. A cloth bag contain numbers 1,2 3,…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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a. Which of the following CANNOT be a probability distribution? Explain.i. p(x) = x / 6 for x = 1,2,3ii. p x = x for x = 1,2,3iii. p(x) = x / 5 for x = 1,0,1 b. An investor has $1000 available for a 1-year investment. The investor isconsidering the following three options:Option APossible return 30% 20% 0% -20%Probability 25% 40% 20% 15%Option BPossible return 50% 30% 0% -40%Probability 15% 50% 20% 15%Option CGuaranteed return 10%Probability 100%i. Based on the expected returns, which of these options should theinvestor choose?ii. Compute the standard deviations for Option A and Option B. Whichone of options A, B, and C has the least risk (i.e. the smallest standarddeviation), which one has the highest risk? What can you say aboutthe relationship between the expected returns and the risks of financialassets in the normal situation?
Suppose that the random variable xx, shown below, represents the number of speeding tickets a person received in a three-year period. P(x)P(x) represents the probability of a randomly selected person having received that number of speeding tickets during that period. Use the probability distribution table shown below to answer the following questions. xx P(x)P(x) 0 0.3891 1 0.281 2 0.1497 3 0.098 4 0.0471 5 0.0351 6+ 0.0000 Would it be unusual to randomly select a person who has received four or more tickets in a three-year period? A. Yes B. NoIs it correct answer B?
Recal the example in class and also in the notes I sent to you. Work again on the example as follows. Example: Suppose that 2 defective microwaves have been included in a shipment of 6 microwaves. The buyers want to test the 6 microwaves one at a time. Let Y denote the number of defective microwaves is found after 3 random selected ones have been tested. Find the probability distribution for Y. Y = the number of defective microwaves found after 3 have been tested What's the possible value of Y? Y P(Y=y) ? ? Questions: 1- Fill the table above with random variables and corresponding probabilities? 2- Calculate the probability that the buyers can find at least 1 defective microwave after 3 have been tested? 3- Find the probability that buyers cannot find any defective microwave after 3 random ones have been tested?
Find the probability of the indicated event if P(E) = 0.20 and P(F) = 0.40. Find P(E or F) if P(E and F) = 0.20. P(E or F) = (Simplify your answer.)
Suppose the following joint probability table for X and Y. Answer the questions. X 1 3 Total -1 0.02 0.03 0.04 0.09 Y 2.75 0.03 0.15 0.16 0.34 3 0.09 0.15 0.06 0.30 4.55 0.16 0.11 0.27 Total 0.14 0.49 0.37 1.00 What is Var(Y|X = 3) – the conditional variance of Y, given that X = 3? Answer:
Find the following probabilities. You MUST draw, label, and shade a curve for each one. Use the table to complete each probability and state the probability to be unusual if it is less than 0.05 or 5%. A. The area to the left of z = -0.97 and to the right of z = 0.97. B. P(-1.76 < z < 0.34)
Luz has noticed the probability distribution for X = number of cars in line to use the drive-thru ATM when she visits her bank is shown below. X 0 1 2 3 4 P(X) 0.10 0.10 0.40 0.30 0.10 What is the probability mean number of cars in line for the drive-thru ATM when Luz visits her bank?
Let X represent the number of tires with low air pressure on a randomly chosen car. The probability distribution of X is as follows. x 0 1 2 3 4 Px 0.3 0.1 0.1 0.2 0.3
e. P(a number greater than 0) = f. P(10) = g. a 5 or a 2 h. NOT a 2 or a 3 1. a 9 J. a negative number 19. If two dice are rolled one time, find the probability of getting these results.
When rolling two fair six-sided dice, getting a pair of 1s is called “snake eyes.” The probability of getting “snake eyes” on any roll is 1/36. Suppose that a game player rolls the two dice 80 times. Let X = the number of rolls that result in “snake eyes.” Find P(X = 2). Interpret this value in context.
23. Flip six unfair coins where, for each coin, P(H) = 0.20 and P(T)= 0.80. Let X be the total number of heads. Find P(X = 4), the probability of getting 4 heads. A. 0.04536 %3D B. 0.03536 C. 0.02536 D. 0.01536

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