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2. Suppose that is an exponential random variable with pdf f(y)= e), y>0. a. Use Chebyshev's Inequality to get an up...
chebyshev’s inequality Problem 2 Chebyshev's Inequality Suppose that the random variable ? has a Poisson distribution...
chebyshev’s inequality
Problem 2 Chebyshev's Inequality Suppose that the random variable ? has a Poisson distribution with the parameter ? > 0, ~ ?(A). Using the Chebyshev's inequality prove that Problem 3 - Application of the Chebyshev's Inequality Suppose that a player plays a game where he gains a dollar with the probability or loses a dollar with the probability . That is, his gain from one game can be modeled as a random variable fi, such that If the...
Compute the probability that an exponential random variable, i.e. , takes a value more than two...
Compute the probability that an exponential random variable, i.e. , takes a value more than two standard deviations more than it's mean.
Suppose that 1/2 where Z is any random variable with E22c, say, with c> 0 and...
Suppose that 1/2 where Z is any random variable with E22c, say, with c> 0 and a E R fixed, and X is any other random variable. (a) Let e > 0. Use Chebyshev's inequality to show that (b) For what values of does the argument in part (a) prove that Xn converges in probability to X? (c) For the values of α identified in part (b), what other mode of convergence of Xn to X is assured (without any...
Suppose that 1/2 where Z is any random variable with E22c, say, with c> 0 and...
Suppose that 1/2 where Z is any random variable with E22c, say, with c> 0 and a E R fixed, and X is any other random variable. (a) Let e > 0. Use Chebyshev's inequality to show that (b) For what values of does the argument in part (a) prove that Xn converges in probability to X? (c) For the values of α identified in part (b), what other mode of convergence of Xn to X is assured (without any...
Let X be a random variable following a continuous uniform distribution from 0 to 10. Find...
Let X be a random variable following a continuous uniform distribution from 0 to 10. Find the conditional probability P(X >3 X < 5.5). Chebyshev's theorem states that the probability that a random variable X has a value at most 3 standard deviations away from the mean is at least 8/9. Given that the probability distribution of X is normally distributed with mean ji and variance o”, find the exact value of P(u – 30 < X < u +30).
1) Let X and Y be random variables. Show that Cov( X + Y, X-Y) Var(X)--Var(Y)...
1) Let X and Y be random variables. Show that Cov( X + Y, X-Y) Var(X)--Var(Y) without appealing to the general formulas for the covariance of the linear combinations of sets of random variables; use the basic identity Cov(Z1,22)-E[Z1Z2]- E[Z1 E[Z2, valid for any two random variables, and the properties of the expected value 2) Let X be the normal random variable with zero mean and standard deviation Let ?(t) be the distribution function of the standard normal random variable....
for Question 4 only parts a and b e Vector Calculus 6t SI vector Calculus (9...
for Question 4 only parts a and b
e Vector Calculus 6t SI vector Calculus (9 x)OHw#5 x\e Modern Mathema× * probability-usinx -0 × × \ Welcome to the L \爽welcome to the LX Secure | https://uncc.instructure.com/courses/72445/assignments/352345?module-itemidz1221488 1, Sec 6.2 #14 2, Sec 6.3 #28, 30, 32, 42, 44 3, Sec 6.4 #48 4. We want to estimate the mean of a certain population. We know that the variance is 2. We get a random sample of size n from...
2. -30 a) The joint pdf of random variables X and Y is given by f(x,y)...
2. -30 a) The joint pdf of random variables X and Y is given by f(x,y) = 27ye-3 y<x<0, y >0. Show that the joint moment generating function(mgf) of X and Y is 27 M(t1, tz) = tı <3, tı + t, <3 (3 - tı) (3 - 7ı - t2) Use the joint mgf to obtain Cov(X,Y). b) Let X1, X2, X3 be independent random variables representing the lifetime of 3 electronic components with the following pdf, where X...
Q5. Suppose the joint pdf of X, Y is given by f(x, y) zy/3 if 0...
Q5. Suppose the joint pdf of X, Y is given by f(x, y) zy/3 if 0 s S1 and 0 sy< 2 and f(x,y) elsewhere. a. Compute P(X+Y2 1). b. What is the probability that (X, Y) E A where A is the region bounded above by the parabola y 2 c. What is the probability that both X, Y exceeding 0.5? d. What is the probability X will take on values that are at least 0.2 units less than...
Problem #3. X is a random variable with an exponential distribution with rate 1 = 3...
Problem #3. X is a random variable with an exponential distribution with rate 1 = 3 Thus the pdf of X is f(x) = le-ix for 0 < x where = 3. a) Using the f(x) above and the R integrate function calculate the expected value of X. b) Using the dexp function and the R integrate command calculate the expected value of X. c) Using the pexp function find the probability that .4 SX 5.7 d) Calculate the probability...
chebyshev’s inequality
Problem 2 Chebyshev's Inequality Suppose that the random variable ? has a Poisson distribution with the parameter ? > 0, ~ ?(A). Using the Chebyshev's inequality prove that Problem 3 - Application of the Chebyshev's Inequality Suppose that a player plays a game where he gains a dollar with the probability or loses a dollar with the probability . That is, his gain from one game can be modeled as a random variable fi, such that If the...
Suppose that 1/2 where Z is any random variable with E22c, say, with c> 0 and a E R fixed, and X is any other random variable. (a) Let e > 0. Use Chebyshev's inequality to show that (b) For what values of does the argument in part (a) prove that Xn converges in probability to X? (c) For the values of α identified in part (b), what other mode of convergence of Xn to X is assured (without any...
Suppose that 1/2 where Z is any random variable with E22c, say, with c> 0 and a E R fixed, and X is any other random variable. (a) Let e > 0. Use Chebyshev's inequality to show that (b) For what values of does the argument in part (a) prove that Xn converges in probability to X? (c) For the values of α identified in part (b), what other mode of convergence of Xn to X is assured (without any...
Let X be a random variable following a continuous uniform distribution from 0 to 10. Find the conditional probability P(X >3 X < 5.5). Chebyshev's theorem states that the probability that a random variable X has a value at most 3 standard deviations away from the mean is at least 8/9. Given that the probability distribution of X is normally distributed with mean ji and variance o”, find the exact value of P(u – 30 < X < u +30).
1) Let X and Y be random variables. Show that Cov( X + Y, X-Y) Var(X)--Var(Y) without appealing to the general formulas for the covariance of the linear combinations of sets of random variables; use the basic identity Cov(Z1,22)-E[Z1Z2]- E[Z1 E[Z2, valid for any two random variables, and the properties of the expected value 2) Let X be the normal random variable with zero mean and standard deviation Let ?(t) be the distribution function of the standard normal random variable....
for Question 4 only parts a and b
e Vector Calculus 6t SI vector Calculus (9 x)OHw#5 x\e Modern Mathema× * probability-usinx -0 × × \ Welcome to the L \爽welcome to the LX Secure | https://uncc.instructure.com/courses/72445/assignments/352345?module-itemidz1221488 1, Sec 6.2 #14 2, Sec 6.3 #28, 30, 32, 42, 44 3, Sec 6.4 #48 4. We want to estimate the mean of a certain population. We know that the variance is 2. We get a random sample of size n from...
2. -30 a) The joint pdf of random variables X and Y is given by f(x,y) = 27ye-3 y<x<0, y >0. Show that the joint moment generating function(mgf) of X and Y is 27 M(t1, tz) = tı <3, tı + t, <3 (3 - tı) (3 - 7ı - t2) Use the joint mgf to obtain Cov(X,Y). b) Let X1, X2, X3 be independent random variables representing the lifetime of 3 electronic components with the following pdf, where X...
Q5. Suppose the joint pdf of X, Y is given by f(x, y) zy/3 if 0 s S1 and 0 sy< 2 and f(x,y) elsewhere. a. Compute P(X+Y2 1). b. What is the probability that (X, Y) E A where A is the region bounded above by the parabola y 2 c. What is the probability that both X, Y exceeding 0.5? d. What is the probability X will take on values that are at least 0.2 units less than...
Problem #3. X is a random variable with an exponential distribution with rate 1 = 3 Thus the pdf of X is f(x) = le-ix for 0 < x where = 3. a) Using the f(x) above and the R integrate function calculate the expected value of X. b) Using the dexp function and the R integrate command calculate the expected value of X. c) Using the pexp function find the probability that .4 SX 5.7 d) Calculate the probability...
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