Nothing Special   »   [go: up one dir, main page]
Scribd Logo
Upload

Welcome to Scribd!

  • 25 views

    Exercises 1

    Uploaded by

    Nguyễn Quỳnh
    1. This document contains 9 practice problems involving concepts in probability and statistics such as calculating probabilities, expected values, variance, and working with probability distribution functions. 2. The problems cover a range of topics including conditional probability, binomial and normal distributions, defective items in production, and defining and working with probability density functions. 3. Solving these problems requires applying formulas and concepts related to probability, random variables, distributions, and descriptive statistics.

    Copyright:

    © All Rights Reserved
    Download as DOCX, PDF, TXT or read online from Scribd

    Exercises 1

    Uploaded by

    Nguyễn Quỳnh
    25 views2 pages
    1. This document contains 9 practice problems involving concepts in probability and statistics such as calculating probabilities, expected values, variance, and working with probability distribution functions. 2. The problems cover a range of topics including conditional probability, binomial and normal distributions, defective items in production, and defining and working with probability density functions. 3. Solving these problems requires applying formulas and concepts related to probability, random variables, distributions, and descriptive statistics.

    Original Description:

    Copyright

    © © All Rights Reserved

    Available Formats

    DOCX, PDF, TXT or read online from Scribd

    Did you find this document useful?

    Is this content inappropriate?

    1. This document contains 9 practice problems involving concepts in probability and statistics such as calculating probabilities, expected values, variance, and working with probability distribution functions. 2. The problems cover a range of topics including conditional probability, binomial and normal distributions, defective items in production, and defining and working with probability density functions. 3. Solving these problems requires applying formulas and concepts related to probability, random variables, distributions, and descriptive statistics.

    Copyright:

    © All Rights Reserved
    Download as DOCX, PDF, TXT or read online from Scribd
    Download as docx, pdf, or txt
    25 views2 pages

    Exercises 1

    Uploaded by

    Nguyễn Quỳnh
    1. This document contains 9 practice problems involving concepts in probability and statistics such as calculating probabilities, expected values, variance, and working with probability distribution functions. 2. The problems cover a range of topics including conditional probability, binomial and normal distributions, defective items in production, and defining and working with probability density functions. 3. Solving these problems requires applying formulas and concepts related to probability, random variables, distributions, and descriptive statistics.

    Copyright:

    © All Rights Reserved
    Download as DOCX, PDF, TXT or read online from Scribd
    Download as docx, pdf, or txt
    of 2

    Faculty of Basic Sciences Probability and Statistics exercises

    Department of Mathematics

    1. In a school, 48% of the students take a foreign language class and 19% of
    students take both foreign language and technology. What is the probability that
    a student takes technology given that the students takes foreign language?
    2. The test contains 10 questions, each one with available four different answers,
    among which just one is correct. To pass the test at least 5 questions must be
    answered correctly. What is the probability that completely unprepared student
    will pass the test ?
    3. In the class of 30 students, seven of them don't have done the homework. The
    teacher choosed randomly 6 students. What is the chance that at least four of
    them have done their homework ?
    4. Three shooters shoot at the same target, each of them shoots just once. The first
    one hits the target with a probability of 70%, the second one with a probability
    of 80% and the third one with a probability of 90%. What is the probability that
    the shooters will hit the target
    a) at least once
    b) at least twice ?
    5. Based on incidence rate, the following table presents the corresponding numbers
    per 100,000 people.

    Sympto Cancer
    Total
    m No Yes

    No 99989 0 99989

    Yes 10 1 11

    Total 99999 1 100000


    Which can then be used to calculate the probability of having cancer when you
    have the symptoms:
    6. A factory produces an item using three machines—A, B, and C—which account
    for 20%, 30%, and 50% of its output, respectively. Of the items produced by
    machine A, 5% are defective; similarly, 3% of machine B's items and 1% of
    machine C's are defective. If a randomly selected item is defective, what is the
    probability it was produced by machine C?
    7. X is a discrete random variable. The table below defines a probability
    distribution for X

    X 0 1 2 3
    P 0.17 0.14 0.36 0.33

    What is the expected value of X? What is the variance value of X?


    8. The random variable X is given by the following PDF. Check that this is a valid
    PDF and calculate the expected, the variance, the standard deviation values of X.

    9. Let X be a continuous random variable with the following


    −x
    f ( x )= c e if x ≥ 0
    { 0 otherwise

    where c is a positive constant.


    a. Find c.
    b. Find the cumulative distribution function of X.
    c. Find P(1<X<3).

    You might also like