Given the normally distributed random variable x with σ=15 and P(x ≤ 50) = .9904, find μ.
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Q: A random sample of size n1 = 14 is selected from a normal population with a mean of 76 and a…
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A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts(That is, pmf…
Q: The distribution function of the random variable Y is given 9. 1 y2 0; y 2 3 - Fy (y) = e.w.
A: To find P(Y≤5) and P(Y>8) by the distribution function.
Q: A random sample of size n₁ = 14 is selected from a normal population with a mean of 75 and a…
A: It is given that: Form the first population: n1 sample size=14μ1 population mean=75σ1 population…
Q: B2. Let A₁,..., An> 0 and let X₁,..., Xn be independent random variables with common mean E(X) = μ…
A: This question deals with the minimum variance of the estimator μ^(X1,X2,...,Xn) for the mean μ given…
Q: 2. Let X be a random variable with E[X] = 15 and Var[X] = 10. Suppose Y = 2X – 7, Use the properties…
A: Given,E(X)=15Var(X)=10and Y=2X-7
Q: m(t) = 2e', defined for t e IR.
A: The mgf can be regarded as the generalization of the pgf.
Q: Suppose a simple random sample of size n=10 is obtained from a population with μ=62 and σ=17
A: Answer Population mean = 62Population standard deviation = 17The sample size = 10
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A: Given that X and Y be random variable such that the mean and variance of X are 2 and 4.…
Q: For an SRS {Y: 3;=, from the normal distribution. Si= 1 fy (y;u, 0²) = ==// (Y-M) 2² 2 e √22√52 Show…
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Q: 2.2. An independent random of sample size 9 is taken from ux = 0²x= 3. A random sample size 25 is…
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Q: C2. Let X be a random variable. (a) Let YaX be another random variable. What is EY, in terms of μ =…
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Q: For a Gaussian random variable with = 0 and ₁=1, what is P(| X > 2) and P[X>2]?
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Q: Let Y1, Y2, Yn be a random sample from a Gamma distribution with parameters a = 1 and ...) B = 0 >…
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Q: Assume that the random variable x is normally distributed with mean u 70 and standard %D deviation o…
A: We have given that. X~N( μ , ?^2 ) μ = 70, ? = 10 Z-score =( x - μ )/?
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Q: A random sample of size n₁ = 14 is selected from a normal population with a mean of 74 and a…
A: μX1 = μX1 = 74σX1 =σX1n1 =614 = 1.603567Similarly,μX2 = μX2 = 69σX2 =σX1n1 =146 = 5.715476Let X =…
Q: Given the normally distributed random variable X with σ = 5 and P(X ≥ 25)=.0526, find µ.
A: We have given that. X~N( μ , ?^2 ) μ = ? , ? = 5 Z-score =( x - μ )/?
Q: Suppose a simple random sample of size n=40 is obtained from a population with μ=63 and σ=14.…
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Q: A sample of n=36 observations is drawn from a normal population with μ=950 and σ=230. Find each of…
A: μ=950 and σ=230
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A: Given information Sample mean x̅ = 0.4365 Population mean µ = 0.5 Sample size = 100 Standard…
Q: Suppose a simple random sample of size n=10is obtained from a population with μ=67 and σ=18. mean is…
A: Given that. X~N( μ , ?^2 ) μ=67 , ?=18 , n=10 Z-score =( x - μ )/?
Q: Assume that a simple random sample has been selected from a normally distributed population. Test…
A: Solution : = 145 = 150 s =13.6 n = 40
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A: Given: Box 1 n (white balls) = 4 n (black balls) = 1 Total number of balls = 5 Box 2 n (white) = 2 n…
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A: Solution
Q: Suppose X is a normal random variable with mean µ and standard deviation σ. Find the number r such…
A: It is an important part of statistics . It is widely used .
Q: Assume the random variable X is normally distributed with a mean μ = 50 and standard deviation σ =…
A: Plug in all the values in the formula, we get
Q: Let y1, ., Yn be a simple random sample of size n from UTM students. Assume that the population size…
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Q: Let X is Normally (Gaussian) distributed with mean 3 and variance 25. Compute the following, P(X>7)…
A: It is given that Mean, μ = 3 Variance, σ2 = 25 Standard deviation, σ = 5 Z-Score, Z = ( X - μ )/σ…
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- 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. Σx = 438, Σy = 275, Σx2 = 32264, Σy2 = 12727, Σxy = 20231, and r ≈ 0.827. x 67 64 75 86 73 73 y 42 39 48 51 44 51 Use a 5% level of significance to test the claim that ρ > 0. (Round your answers to two decimal places.) t critical t Conclusion Reject the null hypothesis, there is sufficient evidence that ρ > 0. Reject the null hypothesis, there is insufficient evidence that ρ > 0. Fail to reject the null hypothesis, there is insufficient evidence that ρ > 0. Fail to reject the null hypothesis, there is sufficient evidence that ρ > 0. Se ≈ 3.1191, a ≈ 6.564, b ≈ 0.5379, and x ≈ 73.000. Find…Assume the MR model: Y = 3 + 4x1 + 5x2 + epsilon, with sigma = 5 Select the Excel command that will find P(Y < 18) when X₁ = 2 and X₂ = 1. (Note: epsilon is the random error term and sigma is the population standard deviation)The distribution of the binomial random variable (X) has the following parametes: P=0,3 and n=9. Determine P(X>2) OA. 0.9160 OB. 0,1960 OC. 0,1715 OD. 1
- Let x be a random variable that has a distribution with mean μ = 150 and standard deviation σ = 15.3. For samples of size n = 36 the sampling distribution of i s with mean = and standard deviation = .Let m denote margin of error, n sample size and σ standard deviation. m= zα/2(σn) Solve the above equation for n.A random sample of size n1 = 15 is selected from a normal population with a mean of 75 and a standard deviation of 9. A second random sample of size n2 = 9 is taken from another normal population with mean 69 and standard deviation 15. Let X1 and X2 be the %3D two sample means. Find: (a) The probability that X - X2 exceeds 3. (b) The probability that 4.9 < X – X2 < 5.9. Round your answers to two decimal places (e.g. 98.76). (a) i (b)
- Assume the random variable X is normally distributed with a mean of μ=50μ=50and a standard deviation of σ=7.σ=7.Compute and find the probability P(X>35).Let the following simple random sample X1, X2, · · , X11 following: 1. Binomial pmf. (11, ¾); 2. Uniform pmf; 3. Uniform pdf (0, a); 4. Exponential pdf with (µ). Find the corresponding pmf/pdf of Y1 , Y4, Y7 and F(Y;) where Yi < Y½ < .. < Y6 < ..< Yı1.3. Let X1, .… , Xn be a random sample. Find the mle of 0 for the cases that the population pdf/pmf is, f(r;:0) = 0, %3D otherwise
- Suppose x has a distribution with μ = 11 and σ = 3. If a random sample of size n = 62 is drawn, find μx, σ x and P(11 ≤ x ≤ 13). (Round σ x to two decimal places and the probability to four decimal places.)μx = σ x = P(11 ≤ x ≤ 13) =When taking random samples of n observations from a population that is not normally distributed, the sampling distribution, x, will be approximately normally distributed never. The population itself must be normally distributed for x to be normally distributed. when the population distribution has low kurtosis. always. when the population standard deviation, o, is greater than n. when n is sufficiently large.A random sample of size n₁ = 14 is selected from a normal population with a mean of 76 and a standard deviation of 7. A second random sample of size n₂ = 9 is taken from another normal population with mean 71 and standard deviation 11. Let X₁ and X₂ be the two sample means. Find: (a) The probability that X₁ – X₂ exceeds 4. 1 2 (b) The probability that 4.3 ≤ X₁ – X2 ≤ 5.6. Round your answers to two decimal places (e.g. 98.76). (a) i (b) i