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H.W. #5 - Q #8:
8. Suppose that n-48 seeds are planted and suppose that each...
QUESTION 5 The probability that a seed will germinate is 0.36. Suppose 178 seeds are planted....
QUESTION 5 The probability that a seed will germinate is 0.36. Suppose 178 seeds are planted. Use the Central Limit Theorem to determine the probability that at most 61 seeds germinate.
1. There are times when a shifted exponential model is appropriate. That is, let the pdf of X be ...
1. There are times when a shifted exponential model is appropriate. That is, let the pdf of X be (a) Find the cdf of X. (b) Find the mean and variance of X. 2. Suppose X is a Gamma random variable with pdf 「(a)go Show that the moment generating function is M(t) 3, Let X equal the nurnber out of n 48 mature aster seeds that will germinate when p- 0.75 is the probability that a particular seed germinates. Approximate...
Let X1, X2, ..., X48 denote a random sample of size n = 48 from the...
Let X1, X2, ..., X48 denote a random sample of size n = 48 from the uniform distribution U(?1,1) with pdf f(x) = 1/2, ?1 < x < 1. E(X) = 0, Var(X) = 1/3 Let Y = (Summation)48, i=1 Xi and X= 1/48 (Summation)48, i=1 Xi. Use the Central Limit Theorem to approximate the following probability. 1. P(1.2<Y<4) 2. P(X< 1/12)
Problem 8 (4x4 pts) Suppose Xi, X2-, ..,. Xn are each independent Poisson random variables with...
Problem 8 (4x4 pts) Suppose Xi, X2-, ..,. Xn are each independent Poisson random variables with mean 1. Let 100 k=1 (a) Rccall, Markov's incquality is P(Y > a) for a> 0 Using Markov's inequality, estimate the probability that P(Y > 120). (b) Rccal, Chebyshev's incquality is Using Chebyshev's inequality, estimate P( Y-?> 20) (c), (d) Using the Central Limit Theorem, estimate P(Y > 120) and Ply-? > 20).
by central limit theorem 12. Suppose that X1, X2, ..., X 40 denote a random sample...
by
central limit theorem
12. Suppose that X1, X2, ..., X 40 denote a random sample of measurements on the proportion of impurities in iron ore samples. Let each variable X have a probability density function given by 132 0<x<1 o elsewhere The ore is to be rejected by the potential buyer if sample of size 40 X, exceeds 2.8. Estimate P ., X. > 2.8) for the
suppose x is the mean of a random sample of size n=36 from the chi-squared distribution...
suppose x is the mean of a random sample of size n=36 from the chi-squared distribution with 18 degrees of freedom. use the central limit theorem to approximate the probability P(16 < x < 20) ?
8. (15 points) Let X ~ Binomial(30,0.6). (a) (5 points) Using the Central Limit Theorem (CLT),...
8. (15 points) Let X ~ Binomial(30,0.6). (a) (5 points) Using the Central Limit Theorem (CLT), approximate the probability that P(X > 20). (b) (5 points) Using CLT, approximate the probability that P(X = 18). (c) (5 points) Calculate P(X = 18) exactly and compare to part(b).
Find the sampling error: u = -5, B = -2.5, n= 100 -7.5 -2.5 0.25 2.5...
Find the sampling error: u = -5, B = -2.5, n= 100 -7.5 -2.5 0.25 2.5 Find M, and o, the mean and standard deviation of the sampling distribution of x: H= 25, 0=5, n= 10. M =25, o,=0.5 M =25, o,=1.58 M=2.5, o,=0.5 My=7.91, o,=1.58 B) A) Assume that the random variable X is normally distributed with mean = 52 and standard deviation = 10. Let n = 25. Find P(x>50). -0 0.16 0.84 D) A) B) C) D)...
Suppose we have 5 independent and identically distributed random variables X1, X2, X3, X4,X5 each with...
Suppose we have 5 independent and identically distributed random variables X1, X2, X3, X4,X5 each with the moment generating function 212 Let the random variable Y be defined as Y = Σ Find the probability that Y is larger than 9. Prove that the distribution you use is the exact distribution, nota Central Limit Theorem approximation
in the north racial violence 1. (15pts) Consider the following data: 2 4 5 6 8...
in
the north racial violence
1. (15pts) Consider the following data: 2 4 5 6 8 P(x) 0.1 0.1 0.3 0.2 0.2 0.1 Step 1: The Expected Value E(X) is Round your answer to one decimal. Step 2: The Variance is Round your answer to at least two decimal places. Step 3: The Standard Deviation is Round your answer to at least two decimal places. Step 4: The value of POX>5) is Round your answer to one decimal. Step 5...
QUESTION 5 The probability that a seed will germinate is 0.36. Suppose 178 seeds are planted. Use the Central Limit Theorem to determine the probability that at most 61 seeds germinate.
1. There are times when a shifted exponential model is appropriate. That is, let the pdf of X be (a) Find the cdf of X. (b) Find the mean and variance of X. 2. Suppose X is a Gamma random variable with pdf 「(a)go Show that the moment generating function is M(t) 3, Let X equal the nurnber out of n 48 mature aster seeds that will germinate when p- 0.75 is the probability that a particular seed germinates. Approximate...
Problem 8 (4x4 pts) Suppose Xi, X2-, ..,. Xn are each independent Poisson random variables with mean 1. Let 100 k=1 (a) Rccall, Markov's incquality is P(Y > a) for a> 0 Using Markov's inequality, estimate the probability that P(Y > 120). (b) Rccal, Chebyshev's incquality is Using Chebyshev's inequality, estimate P( Y-?> 20) (c), (d) Using the Central Limit Theorem, estimate P(Y > 120) and Ply-? > 20).
by
central limit theorem
12. Suppose that X1, X2, ..., X 40 denote a random sample of measurements on the proportion of impurities in iron ore samples. Let each variable X have a probability density function given by 132 0<x<1 o elsewhere The ore is to be rejected by the potential buyer if sample of size 40 X, exceeds 2.8. Estimate P ., X. > 2.8) for the
8. (15 points) Let X ~ Binomial(30,0.6). (a) (5 points) Using the Central Limit Theorem (CLT), approximate the probability that P(X > 20). (b) (5 points) Using CLT, approximate the probability that P(X = 18). (c) (5 points) Calculate P(X = 18) exactly and compare to part(b).
Find the sampling error: u = -5, B = -2.5, n= 100 -7.5 -2.5 0.25 2.5 Find M, and o, the mean and standard deviation of the sampling distribution of x: H= 25, 0=5, n= 10. M =25, o,=0.5 M =25, o,=1.58 M=2.5, o,=0.5 My=7.91, o,=1.58 B) A) Assume that the random variable X is normally distributed with mean = 52 and standard deviation = 10. Let n = 25. Find P(x>50). -0 0.16 0.84 D) A) B) C) D)...
Suppose we have 5 independent and identically distributed random variables X1, X2, X3, X4,X5 each with the moment generating function 212 Let the random variable Y be defined as Y = Σ Find the probability that Y is larger than 9. Prove that the distribution you use is the exact distribution, nota Central Limit Theorem approximation
in
the north racial violence
1. (15pts) Consider the following data: 2 4 5 6 8 P(x) 0.1 0.1 0.3 0.2 0.2 0.1 Step 1: The Expected Value E(X) is Round your answer to one decimal. Step 2: The Variance is Round your answer to at least two decimal places. Step 3: The Standard Deviation is Round your answer to at least two decimal places. Step 4: The value of POX>5) is Round your answer to one decimal. Step 5...
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