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

Choose an American household at random and let the random variable ?X be the number of cars (including SUVs and light trucks) they own. Given is the probability distribution if we ignore the few households that own more than 5 cars. Number of cars 0 1 2 3 4 5 Probability 0.09 0.36 0.35 0.13 0.05 0.02 About what percentage of households have a number of cars within 2 standard deviations of the mean?
When conducting research on allergic reactions to a new drug, a researcher forms random groups with five males in each group. The random variable x is the number of males in the group who develop an allergic reaction. x P(x) 0 0.665 1 0.278 2 0.052 3 0.004 4 0.001 5 0.000 a. Find its mean and standard deviation. (Round to one decimal place as needed) b. What is the probability of at least 3 males developing an allergic reaction? (Round to three decimal places as needed)
A surgery has a success rate of 90%. Suppose that the surgery is performed on threepatients Graph the probability distribution for X using a histogram.Find the mean of X.Find the variance and standard deviation of X.
Suppose 2 dice are rolled, and suppose the discrete variable x counts the number of 3’s that show up. Plot the probability distribution for x using a bar graph. What is the expected value for the random variable x? What is the variance for the random variable x?
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…
Use the probability distribution to complete parts (a) and (b) below. The number of defects per 1000 machine parts inspected Defects 1 4 Probability 0.262 0.299 0.233 0.153 0.037 0.016 ... (a) Find the mean, variance, and standard deviation of the probability distribution. The mean is 1.5. (Round to one decimal place as needed.) The variance is (Round to one decimal place as needed.)
Two chips are drawn at random from a bowl containing 2 white and 3 red chips. Let ?=X=the number of red chips drawn. (a) Write down the probability distribution for ?X. (b) What is the expected value of ?X? (c) Compute the standard deviation of ?X.
Renee and Thomas live at the beach and collect seashells. The number of shells Renee collects on any given day, R, is approximately Normal with a mean of 58.2 shells and a standard deviation of 12.8 shells. The number of shells Thomas collects on any given day, T, is approximately Normal with a mean of 47.9 shells and a standard deviation of 11.5 shells. Assume the two random variables are independent of each other. What is the probability that on a randomly selected day the total number of shells collected by Renee and Thomas is 120 or more? 0.002 0.209 0.284 0.791
• 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.
X is a normally distributed random variable with mean 62 and standard deviation 13. What is the probability that X is between 36 and 88? Use the 0.68-0.95-0.997 rule and write your answer as a decimal.
Service time for a customer coming through a checkout counter in a retail store is a random variable with the mean of 1.0 minutes and standard deviation of 0.5 minutes. Suppose that the distribution of service time is fairly close to a normal distribution. Suppose there are two counters in a store, n = 11 customers in the first line and n2 = 30 customers in the second line. Find the probability that the difference between the mean service time for the shorter line X1 and the mean service time for the longer one X2 is more than 0.5 minutes. Assume that the service times for each customer can be regarded as independent random variables. Round your answer to two decimal places (e.g. 98.76). P = i
The owner of a farmer's market was interested in determining how many oranges a person buys when they buy oranges. He asked the cashiers over a weekend to count how many oranges a person bought when they bought oranges and record this number analysis at a later time. The data is given below in the table. The random variable x represents the number of oranges purchased and P(x) represents the probability that a customer will buy x oranges. Determine the variance of the number of oranges purchased by a customer. Round to two decimal places. X P(x) 1 0.05 O A. 0.56 OB. 3.97 OC. 3.57 OD. 1.95 2 3 0.19 0.20 4 5 0.25 0.12 6 0.10 7 8 0 0.08 9 10- 0 0.01

SEE MORE QUESTIONS

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