14. Find the expected value of a random variable having the following probability distribution:1350.19 0.12 0.03a. 2.033b. 0.904c. -0.360d. 0.408e. 1.773xP(X=x)-40.15-20.2300.28

Question 14)The probability distribution of the random variable is,…

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A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Given that X and Y are independent random variables with the joint probability distribution to the right. Complete parts (a) and (b) below. 4. 0.28 0.175 0.245 f(x.y) 1 0.12 3 0.075 0.105 y (a) Find E(5X -8Y). E(5X-8Y) = (Type an integer or a decimal. Do not round.) %3! (b) Find E(XY). EXY)= (Type an integer or a decimal. Do not round.)
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)
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2. The number of patients visiting an emergency room during the graveyard shift (11:00pm-7:00pm), denoted by the random variable X, has the following probability distribution: 1 2 3 4 5 P(X=x) .05 .20 .25 .20 .10 .15 .05 a. Find the probability there will be 3 or more emergency room patients during a randomly selected 8-hour graveyard shift. b. Find the probability there will be an even number of patients. c. Find the probability there will be at least 2 but not more than 5 patients. d. Find the probability there will be less than 2 patients. e. How do you suppose the probability distribution above was obtained?
-4 2 pl 2 3 | 4 1 Let Xbe a random variable with the following probability distribution. 9. Find the mean of the discrete random variable X. C. -0.03 A. -0.02 B. -0.20 D. -0.30 10. What is a? A. 3.94 C. 3.96 B. 3.95 D. 3.97
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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
Consider the following probability distribution of the random variable x. 15 20 25 30 f(x) 0.11 0.19 0.31 0.39 Find the variance of the random variable x. Select one: Оа. 25.10 оb. 20.69 O C. 24.90 O d. 24.70 O e. 25.49 O f. 24.10 O g. 26.49 O h. 24.41

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14. Find the expected value of a random variable having the following probability distribution: -2 1 3 0 0.23 0.28 0.19 0.12 a. 2.033 b. 0.904 c. -0.360 d. 0.408 e. 1.773 X P(X=x) -4 0.15 5 0.03