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4. Suppose thatz~N(0,1) (a) Find the probability that z >1. (b) Find the probability that zS-1.96....
4. Let Z ~ N(0,1) be a standard normal variable. Calculate the probability (a) P(1 <Z...
4. Let Z ~ N(0,1) be a standard normal variable. Calculate the probability (a) P(1 <Z < 2). (b) P(-0.25 < < < 0.8). (c) P(Z = 0). (d) P(Z > -1).
3. Let Z be a continuous random variable with Z-N(0,1). (a) Find the value of P(Z...
3. Let Z be a continuous random variable with Z-N(0,1). (a) Find the value of P(Z <-0.47). (b) Find the value of P(Z < 2.00). Note denotes the absolute value function. (c) Find b such that P(Z > b) = 0.9382. (d) Find the 27th percentile. (e) Find the value of the critical value 20.05-
4.28 If Z ~ N(0,1), find the following probabilities: a. P(Z <1.38) b. P(Z > 2.14)...
4.28 If Z ~ N(0,1), find the following probabilities: a. P(Z <1.38) b. P(Z > 2.14) c. P(-1.27 <Z<-0.48)
Given N(0,1), find: A) P(Z < - 3.35) * Keep your answer in 4 decimal places....
Given N(0,1), find: A) P(Z < - 3.35) * Keep your answer in 4 decimal places. B) P(Z < 0.89) * Keep your answer in 4 decimal places. Given N(0,1), find: A) P(Z > - 2.65) = Keep your answer in 4 decimal places B) P(Z > 1.81) Keep your answer in 4 decimal places
Suppose that X ~ unif(0,1). Find the distribution of Y = (1 – X)-B – 1...
Suppose that X ~ unif(0,1). Find the distribution of Y = (1 – X)-B – 1 for some fixed B> 0. (Name it!)
Given N(0,1), find: A) P(Z < 2.16 OR Z > 4.13) = 0.9842 Keep your answer...
Given N(0,1), find: A) P(Z < 2.16 OR Z > 4.13) = 0.9842 Keep your answer in 4 decimal places. B) P(Z < 2.5 OR Z 2.59) = 0.0012 * Keep your answer in 4 decimal places. C) P(Z < 2.44 OR Z > 2.48) = * Keep your answer in 4 decimal places. D) P(Z < 4.17 OR Z 4.27) = 0 * Keep your answer in 4 decimal places. Doint
[3] 5. Suppose that f: D[0,1] for all z E D[0, 1] D[0,1] is holomorphic, prove...
[3] 5. Suppose that f: D[0,1] for all z E D[0, 1] D[0,1] is holomorphic, prove that \f'(z) < 1/(1 - 121)2
(4) Given Z N(0, 1) find the following: (a) P(Z 2 1.4) (b) P(Z> 0.75) (c)...
(4) Given Z N(0, 1) find the following: (a) P(Z 2 1.4) (b) P(Z> 0.75) (c) P(IZI S 2) (d) P(IZ 2 2) (e) Find z such that P(Z < z) = 0.11 (f) Find z such that P(Z > z) = 0.02
Exercise 3 Let f be an analytic function on D(0,1). Suppose that f(z) < 1 for...
Exercise 3 Let f be an analytic function on D(0,1). Suppose that f(z) < 1 for all z € C and f() = 0. Show that G) . (Hint: use the function g(z) = f(2).)
9.) Suppose that X is a continuous random variable with density C(1- if [0,1] px(x) ¡f...
9.) Suppose that X is a continuous random variable with density C(1- if [0,1] px(x) ¡f x < 0 or x > 1. (a) Find C so that px is a probability density function. (b) Find the cumulative distribution of X (c) Calculate the probability that X є (0.1,0.9). (d) Calculate the mean and the variance of X
4. Let Z ~ N(0,1) be a standard normal variable. Calculate the probability (a) P(1 <Z < 2). (b) P(-0.25 < < < 0.8). (c) P(Z = 0). (d) P(Z > -1).
3. Let Z be a continuous random variable with Z-N(0,1). (a) Find the value of P(Z <-0.47). (b) Find the value of P(Z < 2.00). Note denotes the absolute value function. (c) Find b such that P(Z > b) = 0.9382. (d) Find the 27th percentile. (e) Find the value of the critical value 20.05-
4.28 If Z ~ N(0,1), find the following probabilities: a. P(Z <1.38) b. P(Z > 2.14) c. P(-1.27 <Z<-0.48)
Given N(0,1), find: A) P(Z < - 3.35) * Keep your answer in 4 decimal places. B) P(Z < 0.89) * Keep your answer in 4 decimal places. Given N(0,1), find: A) P(Z > - 2.65) = Keep your answer in 4 decimal places B) P(Z > 1.81) Keep your answer in 4 decimal places
Suppose that X ~ unif(0,1). Find the distribution of Y = (1 – X)-B – 1 for some fixed B> 0. (Name it!)
Given N(0,1), find: A) P(Z < 2.16 OR Z > 4.13) = 0.9842 Keep your answer in 4 decimal places. B) P(Z < 2.5 OR Z 2.59) = 0.0012 * Keep your answer in 4 decimal places. C) P(Z < 2.44 OR Z > 2.48) = * Keep your answer in 4 decimal places. D) P(Z < 4.17 OR Z 4.27) = 0 * Keep your answer in 4 decimal places. Doint
[3] 5. Suppose that f: D[0,1] for all z E D[0, 1] D[0,1] is holomorphic, prove that \f'(z) < 1/(1 - 121)2
(4) Given Z N(0, 1) find the following: (a) P(Z 2 1.4) (b) P(Z> 0.75) (c) P(IZI S 2) (d) P(IZ 2 2) (e) Find z such that P(Z < z) = 0.11 (f) Find z such that P(Z > z) = 0.02
Exercise 3 Let f be an analytic function on D(0,1). Suppose that f(z) < 1 for all z € C and f() = 0. Show that G) . (Hint: use the function g(z) = f(2).)
9.) Suppose that X is a continuous random variable with density C(1- if [0,1] px(x) ¡f x < 0 or x > 1. (a) Find C so that px is a probability density function. (b) Find the cumulative distribution of X (c) Calculate the probability that X є (0.1,0.9). (d) Calculate the mean and the variance of X
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