Practical class № 15. Random variables, their types. Distribution laws of random variables
Theoretical questions:
1.Random variables, their types
2.Distribution laws of random variables
3.Numerical characteristics of continuous random variables
Classroom assignments:
1. In the following game, there is a one in 4 chance of winning $80; a one in 4 chance of losing $100; and a one-half chance of coming out even. How much would you be willing to pay to play?
2. How much would you be willing to pay for a lottery ticket with a one in 5,000 chance of winning $1 million dollars, and a 4 in 5,000,000 chance of winning $100,000?
3. If the weight of males is N.D. with μ=150 and σ=10, what is the probability that a male will weight between 140 lbs and 155 lbs? [Important Note: The probability that X is equal to any one particular value is zero – P(X=value) = 0 since the N.D. is continuous.]
4. If IQ is ND with a mean of 100 and a s.d. of 10, what percentage of the population will have
(a) IQs ranging from 90 to 110?
(b) IQs ranging from 80 to 120?
Homework:
Solve problems:
1. Suppose that the average salary of college graduates is N.D. with μ=$40,000 and σ=$10,000.
(a) What proportion of college graduates will earn less than $24,800?
(b) What proportion of college graduates will earn more than $53,500?
(c) What proportion of college graduates will earn between $45,000 and $57,000?
(d) Calculate the 80th percentile.
(e) Calculate the 27th percentile.
2. The GPA of college students is ND with μ=2.70 and σ=0.25.
(a) What proportion of students have a GPA between 2.40 and 2.50?
(b) Calculate the 97.5th percentile.
[97.5% of college students have a GPA below _______?]
(c) Calculate the 10th Percentile. [90% of students will have higher GPAs.]
3. Chains have a mean breaking strength of 200 lbs, σ=20 lbs.
(a) What proportion of chains will have a breaking strength below 180 lbs?
(b) 99% of chains have breaking points below _________? [99th percentile] Hint: 50% have breaking points below 200 lbs which is equal to the population mean. The answer has to be more than 200 lbs. We are on the right side of the Z distribution.
Problems for tsis. Tsis 1. Elements of linear algebra
Problem 1. Calculate the determinant
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Problem 2. Solve the system of linear equations: 1. by matrix method; 2. by Cramer's rule:
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Problem 3. Investigate systems on compatibility and, in case of compatibility, solve them by Gauss's method:
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