The probability distribution of the number of students absent on Mondays, is as follows: X O 1 2 3 4567 f(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)
The probability distribution of the number of students absent on Mondays, is as follows: X O 1 2 3 4567 f(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)
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter12: Probability
Section12.4: Discrete Random Variables; Applications To Decision Making
Problem 1E
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