The probability distribution of the number of students absent on Mondays, is as follows:X O1234567f(x) 0.02 0.03 0.26 0.34 0.22 0.08 0.04 0.01(a) What is the probability that more than 3 students are absent.(b) Compute the expected value of the random variable X. Interpret this expected value.(c) Compute the variance and standard deviation of the random variable X.(d) Compute the expected value and variance of Y :(e) Compute the covariance Cov(X, Y)= 7X+ 3.(f) What is the value of the ratio Cov(X,Y)/Var(X) ?(g) What is the value of Cov(X, Y)/Var(X) for Y = ß0 + ß₁X ?(For this exrcise, you can use excel. No need to show all calculations, just specify the formulas and present the final values.)(a)(b)(c)(d)(e)(f)(g)

(a) The probability that more than 3 students are absent:P(X > 3) = P(X = 4) + P(X = 5) + P(X =…

Answered: The probability distribution of the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

If the random variable x has a Poisson Distribution with mean μ = 3.95, find the probability that x = 16.
The tread life of tires mounted on light-duty trucks follows the normal probability distribution with a population mean of 60,000 miles and a population standard deviation of 4,000 miles. Suppose we select a sample of 90 tires and use a simulator to determine the tread life. What is the likelihood of finding that the sample mean is between 59,050 and 60,950? 0.4878 0.9756 0.9878 0.5122
Suppose a random variable X is best described by a uniform probability distribution with range 0 to 6. Find the value of a that makes the following probability statements true. P( X > a ) = 0.13 P( 2.61 <= X <= a ) =0.03
A person's blood glucose level and diabetes are closely related. Let x be a random variable measured in milligrams of glucose per deciliter (1/10 of a liter) of blood. Suppose that after a 12-hour fast, the random variable x will have a distribution that is approximately normal with mean u = 89 and standard deviation o = 27. Note: After 50 years of age, both the mean and standard deviation tend to increase. For an adult (under 50) after a 12-hour fast, find the following probabilities. (Round your answers to four decimal places.) n USE SALT (a) x is more than 60 (b) x is less than 110 (c) x is between 60 and 110 (d) x is greater than 125 (borderline diabetes starts at 125) Need Help? Watch It Read It
The probability distribution of the random variable X represents the number of hits a baseball player obtained in a game for the 2012 baseball season. 1 2 4 P(x) 0.1666 0.3292 0.2779 0.1492 0.0366 0.0405 The probability distribution was used along with statistical software to simulate 25 repetitions of the experiment (25 games). The number of hits was recorded. Approximate the mean and standard deviation of the random variable X based on the simulation. The simulation was repeated by performing 50 repetitions of the experiment. Approximate the mean and standard deviation of the random variable. Compare your results to the theoretical mean and standard deviation. What propert is being illustrated? Click the icon to view the data tables. Data tables (Round to three decimal places as needed.) Table of the numbers of hits for 25 games Approximate the standard deviation of the random variable X based on the simulation for 25 games. 2 2 4 0 2 SN 1.190 hits 3 1 2 1 (Round to three decimal…
Suppose x is a normally-distributed random variable with mean µ= 50 and standard deviation o=2. Use the table to find the probability that x>55. Express your answer as a decimal. -2.5 -2 -1.5 -1 -0.5 0.5 1 1.5 2.5 Area 0.01 0.02 0.07 0.16 0.31 0.5 0.69 0.84 0.93 0.98 0.99 0.01 с. 0.64 а. d. 0.99 b. 0.98
Suppose Y is normally distributed with mean = -3 and variance equal to 4. Find the probability that Y is less than or equal to -0.3. Hint, you must standardize the random variable. 0.9115 0.4602 0.5832 0.1
• Investment in 5 Internet business ventures • The number of successful ventures has a probability distribution: x 0 1 2 3 4 5 P(x) .002 .029 .132 .309 .360 .168 • Estimate the probability that x falls within 2 standard deviations of the mean.
let X be a random variable and X-B(9,0.49) find the mean (expected value) of the random variable X
Fawns between 1 and 5 months old in Mesa Verde National Park have a body weight that is approximately normally distributed 25.36 kg and standard deviation q = 4.72 kg. Let x be the weight of a fawn in kg. What is the probability that for a fawn chosen at random: with mean u - (a) x is less than 28.88 kg? (b) x is greater than 17.34 kg? (c) x lies between 29.04 and 33.6 kg? -

Recommended textbooks for you

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Mathematics For Machine Technology

Advanced Math

ISBN:

9781337798310

Author:

Peterson, John.

Publisher:

Cengage Learning,

Basic Technical Mathematics

Advanced Math

ISBN:

9780134437705

Author:

Washington

Publisher:

PEARSON

Topology

Advanced Math

ISBN:

9780134689517

Author:

Munkres, James R.

Publisher:

Pearson,

SEE MORE TEXTBOOKS