Problem#1:Anopticalinspectionsystemistodistinguishamongdifferent part types. The probability of aany part is 0.98. Suppose that three parts are inspected and that thecorrectclassification ofclassifications are independent. Let the random variable X denote thenumberofpartsthatarecorrectlyclassified.Determinetheprobability mass function of X.

We want to find probability mass function of X

Answered: Problem#1: An optical inspection system…

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...

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Please answer these three questions. Directions: Construct the probability mass functions of the random variables defined by the following exercises. 1. A green die and a red die are rolled. The random variable X is the number of rolls required until a sum of seven spots is observed for the first time. 2. A box contains one P20 bill, one P50 bill, on P100 bill, one P200 bill, one P500 bill, and one P1,000 bill. Two bills are drawn in succession and without replacement from the box. The random variable T is the total monetary value of the two bills. 3. Four students are applying for a summer job in a fast-food restaurant. The result of the application is that a student may be hired or rejected. Assume that a student is equally likely to be hired or rejected for the job. The random variable X is the number of students among the four who hired.
b) Suppose a single observation X = x is observed where X is a random variable with probability mass function given by the table below 1 2 3 4 P(X = x) 1 1 1+0 1-0 4 4 4 The following 10 independent observations were taken from such a distribution: 4 1 4 2 3 3 3 1 2 3 Find the MME Ô of 0.
Use the probability mass function of a uniform random variable with parameters a and b tofind its mean.
Q1 The travel time (T) from district A to district B in a city may be 0.5, 1.0, 1.5, 2.0, 2.5 or 3. and the corresponding probability mass function is given as shown in the figure below. a) Find the mean value of the travel time. b) Find the modal value. c) Find the variance, standard deviation and coefficient of variation of the travel time. d) What is the probability that the travel time will be less than or equal to 1.5 hour P(T <1.5) =? 0.35 0.30 0.3 0.25 0.25 0.20 0.2 ' 0.15 0.10 0.10 0.1 0.05 0.05 0.5 1 1.5 2 2.5 3 I (hours) (1)'d
Answer the following questions on a separate sheet of paper. 1. Determine if each of the following situations illustrates a continuous random variable or not. weight of a randomly selected grade 11 student a. b. number of Filipino people who will vote in the next national election fastest speed of a randomly selected car racer in a car racing competition С. d. a farmer's record of the number of mongo seeds in a sack
A. Classify each random variable as discrete or continuous. 1. X: Number of women among 20 newly hired teachers 2. Y: Height (in centimeters) of a 30 randomly selected adult males 3. Z: Number of car accidents among 8 selected cities 4. A: Amount of rainfall (in millimeters) in different cities in Metro Manila 5. B: Number of gifts received by 20 students during Christmas season
1. The random variables X and Y describe the outcome of two independent tosses with a dice. Let Z = X+Y be the sum of the results. Determine (a) The probability distributions for X, Y and Z. (b) H(X), H(Y) and H(Z). (c) H(YX), H(Z|X) and H(X|Z). (d) I(X;Y) and I(X; Z).
Choose ALL THE CORRECT STATEMENTS in the following ones about probability distribution. i. Probability mass function indicates the probability distribution of a continuous random variable. ii. Probability mass function indicates the probability distribution of a discrete random variable. iii. The probability mass function of a discrete random variable X at a is denoted by P(X < a). iv. The probability function of a continuous random variable Y can be described by using P(Y= a).
In tests of stopping distances for automobiles, those automobiles traveling at 30 miles per hour before the brakes are applied tend to travel distances that appear to be uniformly distributed between two points a and b. Suppose three automobiles are used in a test. Find the probability that exactly one of the three travels past the midpoint between a and b.
Many random number generators allow users to specify the range of the random numbers to be produced. Suppose you specify that the random number Y can take any value between 0 and 6. Then the density curve of the outcomes has constant height between 0 and 6 and height O elsewhere.

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