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Problem 4 (12 points; 2,2|414) Consider a certain machine part. Let X = lifetime (in days)...
Problem 10 (9 points) The lifetime (in hours) of a replacement part for a machine is...
Problem 10 (9 points) The lifetime (in hours) of a replacement part for a machine is modeled as having a Weibull distribution with parameters a- V2 and ß 20. 2pts i. What are the mean and standard deviation of this Weibull distribution? σ= (round to nearest integer) 2pts . Determine the probability that a single replacement part provides over 25 hours of operation for the machine. P(X > 25) iii. We currently have a supply of 49 replacement parts. Use...
4. Assume the lifetime X (in years) of a copy machine is a continuous random variable...
4. Assume the lifetime X (in years) of a copy machine is a continuous random variable with the pdf below: PDF: p(x) = 5x3e-* defined for x > 0 a) (1.5 pts) Write the integral form for the mean of x. You do not need to compute it. Upper limit Correct function to represent integrand u = E(X) = dx Lower limit b) (1.5 pts) Do the same thing here but for the expected value of X? You do not...
3. A random variable X is said to have a Cauchy(α, β) distribution if and only...
3. A random variable X is said to have a Cauchy(α, β) distribution if and only if it has PDF function Now, suppose that Xi and X2 are independent Cauchy(0, 1) random variables, and let Y = X1 + X2. Use the transformation technique to find and identify the distribution of Y by first finding the joint distribution of Xi and Y. (Seahin 3 4
x 20 The lifetime, in years, of a certain type of pump is a random variable...
x 20 The lifetime, in years, of a certain type of pump is a random variable with probability density function 3 (x+1)+ 0 True (Note: “True" means “Otherwise” or “Elsewere") 1) What is the probability that the pump lasts more than 3 years? 2) What is the probability that the pump lasts between 1 and 2 years? 3) Find the mean lifetime. 4) Find the variance of the lifetime. 5) Find the cumulative distribution function of the lifetime. 6) Find...
please do them both for high rate Problem 3. Let X be a discrete random variable,...
please do them both for high rate
Problem 3. Let X be a discrete random variable, with probability distribution P(X x)0.95, P(Xx2) 0.05 Determine X1 and X2 such that E[X] 0 and σ2(X)-7. Problem 4. The life X, in hours, of a certain device, has a pdf 100 x()t2 2 100 0, t<100 (a) What are the probability that this device will survive 150 hours of operation? (b) Find the life expectancy of the device.
7. Let X a be random variable with probability density function given by -1 < x < 1 fx(x) otherwise (a) Find the...
7. Let X a be random variable with probability density function given by -1 < x < 1 fx(x) otherwise (a) Find the mean u and variance o2 of X (b) Derive the moment generating function of X and state the values for which it is defined (c) For the value(s) at which the moment generating function found in part (b) is (are) not defined, what should the moment generating function be defined as? Justify your answer (d) Let X1,...
Only 1-4) X, be a random sample from N(4,a ), , and let X and S...
Only 1-4)
X, be a random sample from N(4,a ), , and let X and S be sample mean and sample 1. Let variance, respectively. In Order to show that and S are independent, tollow the steps below. and show the joint pdf of X,X3,*, X 1-1) Use the change of variable technique = Nx = x - is (п-1)5? п(т-и? f(E,x,) еxp ov2x 2a2 Use Jacobian for n x n variable transformation 1-2) Use the fact that X~N(u,a n)...
RANU 10 pts. Problem No. 6.4 The lifetime, in years, of a certain type of pump...
RANU 10 pts. Problem No. 6.4 The lifetime, in years, of a certain type of pump is a random variable with probability density function (x+1)* x20 0 True (Note: "True" means "Otherwise" or "Elsewere") 1) What is the probability that the pump lasts more than 3 years? 2) What is the probability that the pump lasts between 1 and 2 years? 3) Find the mean lifetime. 4) Find the variance of the lifetime. 5) Find the cumulative distribution function of...
Problem 7 (15 points). Let X be random variable with the binomial distribution with parameters n...
Problem 7 (15 points). Let X be random variable with the binomial distribution with parameters n and 0 <p<1. (1) Show that **- 1 = 2* for any 1 Sxsn. (2) Show that when 0 < x < (n + 1)p, P(X = x) is an increasing function x and for (n + 1)p <x Sn, P(X = x) is a decreasing function x. (3) A certain basketball player makes a foul shot with probability 0.80. Determine for whal value...
Problem 3 (Needed for Problem 4) A continuous random variable X is said to have an...
Problem 3 (Needed for Problem 4) A continuous random variable X is said to have an exponential distribution, written Exp(X), if its probability density function f is such that le- if > 0 10 if x < 0 f(0) = 0 where > 0 is a real number. 1. Compute the mean of X 2. Compute the variance of X 3. Compute the cumulative distribution function F of X. Use this to show that for any real numbers s and...
Problem 10 (9 points) The lifetime (in hours) of a replacement part for a machine is modeled as having a Weibull distribution with parameters a- V2 and ß 20. 2pts i. What are the mean and standard deviation of this Weibull distribution? σ= (round to nearest integer) 2pts . Determine the probability that a single replacement part provides over 25 hours of operation for the machine. P(X > 25) iii. We currently have a supply of 49 replacement parts. Use...
4. Assume the lifetime X (in years) of a copy machine is a continuous random variable with the pdf below: PDF: p(x) = 5x3e-* defined for x > 0 a) (1.5 pts) Write the integral form for the mean of x. You do not need to compute it. Upper limit Correct function to represent integrand u = E(X) = dx Lower limit b) (1.5 pts) Do the same thing here but for the expected value of X? You do not...
3. A random variable X is said to have a Cauchy(α, β) distribution if and only if it has PDF function Now, suppose that Xi and X2 are independent Cauchy(0, 1) random variables, and let Y = X1 + X2. Use the transformation technique to find and identify the distribution of Y by first finding the joint distribution of Xi and Y. (Seahin 3 4
x 20 The lifetime, in years, of a certain type of pump is a random variable with probability density function 3 (x+1)+ 0 True (Note: “True" means “Otherwise” or “Elsewere") 1) What is the probability that the pump lasts more than 3 years? 2) What is the probability that the pump lasts between 1 and 2 years? 3) Find the mean lifetime. 4) Find the variance of the lifetime. 5) Find the cumulative distribution function of the lifetime. 6) Find...
please do them both for high rate
Problem 3. Let X be a discrete random variable, with probability distribution P(X x)0.95, P(Xx2) 0.05 Determine X1 and X2 such that E[X] 0 and σ2(X)-7. Problem 4. The life X, in hours, of a certain device, has a pdf 100 x()t2 2 100 0, t<100 (a) What are the probability that this device will survive 150 hours of operation? (b) Find the life expectancy of the device.
7. Let X a be random variable with probability density function given by -1 < x < 1 fx(x) otherwise (a) Find the mean u and variance o2 of X (b) Derive the moment generating function of X and state the values for which it is defined (c) For the value(s) at which the moment generating function found in part (b) is (are) not defined, what should the moment generating function be defined as? Justify your answer (d) Let X1,...
Only 1-4)
X, be a random sample from N(4,a ), , and let X and S be sample mean and sample 1. Let variance, respectively. In Order to show that and S are independent, tollow the steps below. and show the joint pdf of X,X3,*, X 1-1) Use the change of variable technique = Nx = x - is (п-1)5? п(т-и? f(E,x,) еxp ov2x 2a2 Use Jacobian for n x n variable transformation 1-2) Use the fact that X~N(u,a n)...
RANU 10 pts. Problem No. 6.4 The lifetime, in years, of a certain type of pump is a random variable with probability density function (x+1)* x20 0 True (Note: "True" means "Otherwise" or "Elsewere") 1) What is the probability that the pump lasts more than 3 years? 2) What is the probability that the pump lasts between 1 and 2 years? 3) Find the mean lifetime. 4) Find the variance of the lifetime. 5) Find the cumulative distribution function of...
Problem 7 (15 points). Let X be random variable with the binomial distribution with parameters n and 0 <p<1. (1) Show that **- 1 = 2* for any 1 Sxsn. (2) Show that when 0 < x < (n + 1)p, P(X = x) is an increasing function x and for (n + 1)p <x Sn, P(X = x) is a decreasing function x. (3) A certain basketball player makes a foul shot with probability 0.80. Determine for whal value...
Problem 3 (Needed for Problem 4) A continuous random variable X is said to have an exponential distribution, written Exp(X), if its probability density function f is such that le- if > 0 10 if x < 0 f(0) = 0 where > 0 is a real number. 1. Compute the mean of X 2. Compute the variance of X 3. Compute the cumulative distribution function F of X. Use this to show that for any real numbers s and...
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