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1. (25 pts. Use the given tables to approximate the following: (a) For a normal random...
Let Z be a standard normal random variable. Use the calculator provided, or this table to...
Let Z be a standard normal random variable. Use the calculator provided, or this table to determine the value of c. P(0.56 37 3c) = 0.2655 Carry your intermediate computations to at least four decimal places. Round your answer to two decimal places. e X 5 ? Use the calculator provided to solve the following problems. . Consider at distribution with 11 degrees of freedom. Compute P(15 1.57). Round your answer to at least three decimal places. . Consider at...
Name 1. This problem is designed to test your skill in using the Tables in the...
Name 1. This problem is designed to test your skill in using the Tables in the Appendix to find probabilities and cutoffs. (Drawing a picture is highly recommended.) (a) Suppose that the random variable B follows a Binomial distribution with no 9 and p = .70, find P(B = 6). (b) Suppose that the random variable z follows the Standard Normal probability distribution, find P(Z 2 -1.27). (C) Suppose that the random variable T follows at distribution with degrees of...
3. Let X be normal random variable and Y be a Chi-square random variable with df...
3. Let X be normal random variable and Y be a Chi-square random variable with df degrees of freedom then the ratio follows (note that this is the reason we use a common test when We don't know for certain the true value of the variance): a) A x?distribution b) A normal distribution c) An F distribution d) At distribution.
2. If X and Y are independent random variables, X has a normal distribution with mean...
2. If X and Y are independent random variables, X has a normal distribution with mean 2 variance 4, and Y has a chi-square distribution with 9 degrees of freedom, then find u such that P(X > 2+11,7)=0.01.
7. Let Xn Xi++X2, where the Xi's are iid standard normal random variables (a) Show that Sn is a c...
7. Let Xn Xi++X2, where the Xi's are iid standard normal random variables (a) Show that Sn is a chi-square random variable with n de- grees of freedom. Hint: Show that X is chi-square with one degree of freedom, and then use Problem 6. (b) Find the pdf of (c) Show that T2 is a Rayleigh random variable. (d) Find the pdf for Ts. The random variable Ts is used to model the speed of molecules in a gas. It...
1. Suppose t hat Xhas t he chi-square distribution on p1∈(0, ∞) degrees of f reedom...
1. Suppose t hat Xhas t he chi-square distribution on p1∈(0, ∞) degrees of f reedom and that, i ndependently, Y has t he chi-square distribution on p2∈(0, p1) degrees of f ree-dom. a. Use moment generating functions to find the distribution of X + Y . b. A naive guess might be that the distribution of X − Y is chi-square on p1− p2 degrees of freedom. Prove that such a guess is wrong by demonstrating that P (X...
1. Suppose t hat Xhas t he chi-square distribution on p1∈(0, ∞) degrees of f reedom...
1. Suppose t hat Xhas t he chi-square distribution on p1∈(0, ∞) degrees of f reedom and that, i ndependently, Y has t he chi-square distribution on p2∈(0, p1) degrees of f ree-dom. a. Use moment generating functions to find the distribution of X + Y . b. A naive guess might be that the distribution of X − Y is chi-square on p1− p2 degrees of freedom. Prove that such a guess is wrong by demonstrating that P (X...
3. If a random variable Y has a Chi-square distribution with 9 degrees of freedom. a)...
3. If a random variable Y has a Chi-square distribution with 9 degrees of freedom. a) The mean of the distribution is b) The standard deviation of the distribution is c) The probability, p( y = 5) = d) The probability, P(Y>8 ) = e) the probability, p( y < 2) = _
Question 2. Consider a random variable X~x20 - Answer the following. i) ii) What are E(X)...
Question 2. Consider a random variable X~x20 - Answer the following. i) ii) What are E(X) and Var(X)? What value is the value xão,0.1 that satisfies P(xão > xão,0.1) = 0.1? Suppose you draw random samples of n=40 individual values from a population where the relative frequency of values follows a Chi-square distribution with 20 degrees of freedom. That is Xi~xão for every random variable in the random sample (X1 , X2 ,... X40). iii) iv) Use the Central Limit...
Prove that if random variable X follows a standard normal distribution (with mean u= 0 and...
Prove that if random variable X follows a standard normal distribution (with mean u= 0 and standard deviation o = 1), then Y = X2 follows a chi-square distribution with 1 degree of freedom. In particular, show that My(t) = Mx2(t) = E[etX?), which equals the moment generating function of a chi-square distribution with 1 degree of freedom.
Let Z be a standard normal random variable. Use the calculator provided, or this table to determine the value of c. P(0.56 37 3c) = 0.2655 Carry your intermediate computations to at least four decimal places. Round your answer to two decimal places. e X 5 ? Use the calculator provided to solve the following problems. . Consider at distribution with 11 degrees of freedom. Compute P(15 1.57). Round your answer to at least three decimal places. . Consider at...
Name 1. This problem is designed to test your skill in using the Tables in the Appendix to find probabilities and cutoffs. (Drawing a picture is highly recommended.) (a) Suppose that the random variable B follows a Binomial distribution with no 9 and p = .70, find P(B = 6). (b) Suppose that the random variable z follows the Standard Normal probability distribution, find P(Z 2 -1.27). (C) Suppose that the random variable T follows at distribution with degrees of...
3. Let X be normal random variable and Y be a Chi-square random variable with df degrees of freedom then the ratio follows (note that this is the reason we use a common test when We don't know for certain the true value of the variance): a) A x?distribution b) A normal distribution c) An F distribution d) At distribution.
2. If X and Y are independent random variables, X has a normal distribution with mean 2 variance 4, and Y has a chi-square distribution with 9 degrees of freedom, then find u such that P(X > 2+11,7)=0.01.
7. Let Xn Xi++X2, where the Xi's are iid standard normal random variables (a) Show that Sn is a chi-square random variable with n de- grees of freedom. Hint: Show that X is chi-square with one degree of freedom, and then use Problem 6. (b) Find the pdf of (c) Show that T2 is a Rayleigh random variable. (d) Find the pdf for Ts. The random variable Ts is used to model the speed of molecules in a gas. It...
3. If a random variable Y has a Chi-square distribution with 9 degrees of freedom. a) The mean of the distribution is b) The standard deviation of the distribution is c) The probability, p( y = 5) = d) The probability, P(Y>8 ) = e) the probability, p( y < 2) = _
Question 2. Consider a random variable X~x20 - Answer the following. i) ii) What are E(X) and Var(X)? What value is the value xão,0.1 that satisfies P(xão > xão,0.1) = 0.1? Suppose you draw random samples of n=40 individual values from a population where the relative frequency of values follows a Chi-square distribution with 20 degrees of freedom. That is Xi~xão for every random variable in the random sample (X1 , X2 ,... X40). iii) iv) Use the Central Limit...
Prove that if random variable X follows a standard normal distribution (with mean u= 0 and standard deviation o = 1), then Y = X2 follows a chi-square distribution with 1 degree of freedom. In particular, show that My(t) = Mx2(t) = E[etX?), which equals the moment generating function of a chi-square distribution with 1 degree of freedom.
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