Let P, Q, R be events in a sample space S and suppose the following: Pr[P] = Pr[Q] = Pr[ R] = 0.30 Pr[ Pn R] = Pr[QnR] = 0.12 Pr[ Pn QnR] = 0.04 . P and Q are independent Find the probability that an outcome selected at random from S belongs to neither P, nor Q, nor R. ● ● ●
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![Let P, Q, R be events in a sample space S and suppose the following:
• Pr[P] = Pr[Q] = Pr[ R] = 0.30
• Pr[ POR] = Pr [QnR] = 0.12
• Pr[ PnQnR] = 0.04
• P and Q are independent
Find the probability that an outcome selected at random from S belongs to neither P, nor Q, nor R.
Enter the requested probability as a decimal rounded to two digits to the right of the decimal point. For example: 0.88
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- Suppose that we have a sample space S = {E1, E2, E3, E4, E5, E6, E7}, where E1, E2, ...E7 denote the sample points. The following probability assignments apply: P(E1) = 0.05, P(E2) = 0.20, P(E3) = 0.20, P(E4) = 0.25, P(E5) = 0.15, P(E6) = 0.10, and P(E7) = .05. Let A = {E1, E4, E6}, B = {E2, E4, E7}, C = {E2, E3, E5, E7}a) Find the P(A), P(B) and P(C), write the answers on the space provided. b) Find B' and P(B')c) Find A U B and P(A U B)Suppose that the response time X of a subject to a stimulus is N(15, 16). If n-16, then the probability of the sample mean greater than 12 is: a. 0.9772 Ob. 0.9987 Oc. 0.0013 Od. 0.7899Let x be a random variable that represents the batting average of a professional baseball player. Let y be a random variable that represents the percentage of strikeouts of a professional baseball player. A random sample of n = 6 professional baseball players gave the following information. x 0.318 0.272 0.340 0.248 0.367 0.269 y 3.4 8.0 4.0 8.6 3.1 11.1 Σx = 1.814, Σy = 38.2, Σx2 = 0.559262, Σy2 = 298.34, Σxy = 10.8736, and r ≈ -0.874. (d) Find the predicted percentage of strikeouts for a player with an x = 0.35 batting average. (Use 2 decimal places.)%(e) Find a 95% confidence interval for y when x = 0.35. (Use 2 decimal places.) lower limit % upper limit % (f) Use a 1% level of significance to test the claim that β ≠ 0. (Use 2 decimal places.) t critical t ±
- Let x be a random variable that represents the percentage of successful free throws a professional basketball player makes in a season. Let y be a random variable that represents the percentage of successful field goals a professional basketball player makes in a season. A random sample of n = 6 professional basketball players gave the following information. x 67 70 69 81 65 86 y 51 54 45 56 50 49 Given that ∑x = 438, ∑y = 305, ∑x2 = 32,332, ∑y2 = 15,579, ∑xy = 22,302, and r = 0.226, find the P-value for a test claiming that ρ is greater than zero. 0.25 > P-value > 0.10 0.10 > P-value > 0.05 0.40 > P-value > 0.25 P-value < 0.0005 P-value > 0.40XQ P.6: On its way, a car meets 4 traffic lights, and the probability that each of them will be red is 0.5. Let X be a discrete random variable equal to the number of traffic lights that were green when the car arrived. X may take the values of 0, 1, 2, 3, 4. (Assume traffic lights are independent.) What is the probability distribution of X? The probability distribution of X is 3 4 p(x) 0.5 0.25 0.125 0.0625 0.0625 The probability of distribution of X is 3 p(x) 0.5 0.5 0.25 0.125 The probability of distribution of X is 3 4 p(x) 0.5 0.25 0.5 0.25 0.125 The probability distribution of X is 1 3 4 p(x) | 0.5 || 0.5 || 0.5 | 0.5 || 0.5 The probability of distribution of X is 3 4 p(x) || 0.0625 0.0625 0.125 0.25 0.5Let x be a random variable that represents the batting average of a professional baseball player. Let y be a random variable that represents the percentage of strikeouts of a professional baseball player. A random sample of n = 6 professional baseball players gave the following information. x 0.318 0.272 0.340 0.248 0.367 0.269 y 3.4 8.0 4.0 8.6 3.1 11.1 Σx = 1.814, Σy = 38.2, Σx2 = 0.559262, Σy2 = 298.34, Σxy = 10.8736, and r ≈ -0.874. (e) Find a 95% confidence interval for y when x = 0.35. (Use 2 decimal places.) lower limit % upper limit (g) Find a 95% confidence interval for β and interpret its meaning. (Use 2 decimal places.) lower limit upper limit
- Questior Let X; - N(3, 4) and suppose that we are going to observe X = {X1, X2, X3, X4, X5, Xg}. Calculate the sample mean and variance for x = {4.3, 5.8, 4.8, 9.8, -0.4, 7.2}. What is the probability of getting a sample mean at least as extreme (that is, greater than) as what we have here? Is the probability of getting a sample variance at least as extreme as the one we have calculated less than 0.1?Let X be a random variable with the following PMF: X = k k=-5 k=-2 k=0 k=2 k=5 P(X=k) 0.3 0.05 0.05 0.2 0.4 What is the probability that X is a negative number. Group of answer choices 0.6 0.4 0.35 1Show that the expectation of the sum of two random variables defined over the same sample space is the sum of the expectations. Hint: Let p1, p2, ··· , pn be the probabilities associated with the n sample points; let x1, x2, ··· , xn, and y1, y2, ··· , yn, be the values of the random variables x and y for the n sample points. Write out E(x), E(y), and E(x + y)
- Let x be a random variable that represents the percentage of successful free throws a professional basketball player makes in a season. Let y be a random variable that represents the percentage of successful field goals a professional basketball player makes in a season. A random sample of n = 6 professional basketball players gave the following information. x 73 74 80 66 77 77 y 50 52 45 46 52 53 Verify that Se ≈ 3.694, a ≈ 38.254, b ≈ 0.153, and , ∑x =447, ∑y =298, ∑x2 =33,419, and ∑y2 =14,858, and use a 5% level of significance to find the P-value for the test that claims that β is greater than zero. Group of answer choices Since the P-value is greater than α = 0.05, we reject the null hypothesis that the population slope β is equal to zero in favor of the alternate hypothesis that the population slope β is greater than zero. Since the P-value is equal to α = 0.05, we fail to reject the null hypothesis that the population slope β is equal to zero in favor of the…Let discrete random variable X represeant the number of addictive substances used by subjects is a study. The following table summarize the frequency distribution for this random variable. (Data are randomly generated) Number of addictive substances used 0 1 2 3 4 5 6 7 8 9 Frequency 153 351 151 81 47 24 10 10 3 1 A subject is selected at random from those involved in the study. Let p₁ be the probability that the subject used 2 addictive substances, p2 the probability that the subject used fewer than 4 addictive substances, p3 the probability that the subject used more than 6 addictive substances, and p4 the probability that the subject used between 5 and 8 addictive substances, inclusive. Then the P₁, P2, P3, and P4 are, respectively, (Choose one from the following which is closest to the correct answer.) O a. 0.1817, 0.8857, 0.0168, 0.0277. O b. 0.1817, 0.8857, 0.0168, 0.0529. e. 0.1817, 0.8857, 0.0289, 0.0566. O d. 0.1817, 0.9422, 0.0168, 0.0566. O c. 0.1817, 0.8857, 0.0168, 0.0566.
