Homework Answers
2)
Given that ,
= 1 / 8
Var(X) = 1 /
2 = 1 / (1/8)2 = 64
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Problem #2: Let X be an exponentially distributed random variable with with 1 = . What...
2. Let X be an exponentially distributed random variable with parameter 1 = 2. Determine P(X...
2. Let X be an exponentially distributed random variable with parameter 1 = 2. Determine P(X > 4). 3. Let X be a continuous random variable that only takes on values in the interval [0, 1]. The cumulative distribution function of X is given by: F(x) = 2x² – x4 for 0 sxsl. (1) (a) How do we know F(x) is a valid cumulative distribution function? (b) Use F(x) to compute P(i sX så)? (c) What is the probability density...
Problem #2: Let y(x) be the solution to the following initial value problem. x4 y' +...
Problem #2: Let y(x) be the solution to the following initial value problem. x4 y' + 5x> y = Inça), x>0, y(1) = 5. Find y(e). Problem #2: O Problem #2: Enter your answer symbolically, as in these examples Just Save Submit Problem #2 for Grading Problem #2 | Attempt #1 | Attempt #2 | Attempt #3 Your Answer: Your Mark:
Let X be an exponentially distributed random variable with parameter value 2. a) Use the...
Let X be an exponentially distributed random variable with parameter value 2. a) Use the markov inequality to estimate P(X >= 3). b) Use the chebyshev inequaity to estimate P(X >= 3). c) Calculate P(X >= 3) exactly.
Problem #3: The velocity of a particle in a gas is a random variable X with...
Problem #3: The velocity of a particle in a gas is a random variable X with probability distribution fx (x) = 343 z2 e-7x x>0. The kinetic energy of the particle is Y = 2 mx2. Suppose that the mass of the particle is 16 yg. Find the probability distribution of Y. (Do not convert any units.) Enter your answer as a symbolic 343/16*sqrt(2*y/16)*(e^(-7*sqrt(2*) function of y, as in these examples Problem #3: 343 V (e-71 (20)/16) + e7V (2/16))...
Problem #4: Let 0 2 A = 2 9 and b = 0 2 4 Find...
Problem #4: Let 0 2 A = 2 9 and b = 0 2 4 Find the least squares solution of the linear system Ax = b. Enter the components of the least squares solution x = [x y]? into the answer box below (in order), separated with a comma. Problem #4: Enter your answer symbolically, as in these examples Just Save Submit Problem #4 for Grading Problem #4 Attempt #1 Attempt #2 Attempt #3 Your Answer: Your Mark:
A random variable X is exponentially distributed with an expected value of 52. a-1. What is...
A random variable X is exponentially distributed with an expected value of 52. a-1. What is the rate parameter λ? (Round your answer to 3 decimal places.) a-2. What is the standard deviation of X? b. Compute P(44 ≤ X ≤ 60). (Round intermediate calculations to at least 4 decimal places and final answer to 4 decimal places.) c. Compute P(41 ≤ X ≤ 63). (Round intermediate calculations to at least 4 decimal places and final answer to 4 decimal...
A random variable X is exponentially distributed with an expected value of 49. a-1. What is...
A random variable X is exponentially distributed with an expected value of 49. a-1. What is the rate parameter λ? (Round your answer to 3 decimal places.) a-2. What is the standard deviation of X? b. Compute P(41 ≤ X ≤ 57). (Round intermediate calculations to at least 4 decimal places and final answer to 4 decimal places.) c. Compute P(34 ≤ X ≤ 64). (Round intermediate calculations to at least 4 decimal places and final answer to 4 decimal...
Problem #2: Let y(t) be the solution to the following initial value problem 6, y'(0)3 y"7y...
Problem #2: Let y(t) be the solution to the following initial value problem 6, y'(0)3 y"7y Find Y(s), the Laplace transform ofy() Enter your answer as a symbolic function of s, as in these examples Problem #2: Submit Problem #2 for Grading Just Save Attempt #3 Problem #2 Attempt # 2 Attempt #5 Attempt#1 Attempt #4 Your Answer: Your Mark
A random variable X is exponentially distributed with a mean of 0.23. a) What is the...
A random variable X is exponentially distributed with a mean of 0.23. a) What is the standard deviation of X? (Round your answer to 2 decimal places.) b) Compute P(X > 0.38). (Round intermediate calculations to at least 4 decimal places and final answer to 4 decimal places.) c) Compute P(0.16 ≤ X ≤ 0.38). (Round intermediate calculations to at least 4 decimal places and final answer to 4 decimal places.)
4. Let X be a continuous exponentially distributed random variable with the intensity equal to 0.54....
4. Let X be a continuous exponentially distributed random variable with the intensity equal to 0.54. Find the probability that X takes of a value from interval (4, 8) thrice in 15 experiments. ir distrihiution laws:
2. Let X be an exponentially distributed random variable with parameter 1 = 2. Determine P(X > 4). 3. Let X be a continuous random variable that only takes on values in the interval [0, 1]. The cumulative distribution function of X is given by: F(x) = 2x² – x4 for 0 sxsl. (1) (a) How do we know F(x) is a valid cumulative distribution function? (b) Use F(x) to compute P(i sX så)? (c) What is the probability density...
Problem #2: Let y(x) be the solution to the following initial value problem. x4 y' + 5x> y = Inça), x>0, y(1) = 5. Find y(e). Problem #2: O Problem #2: Enter your answer symbolically, as in these examples Just Save Submit Problem #2 for Grading Problem #2 | Attempt #1 | Attempt #2 | Attempt #3 Your Answer: Your Mark:
Problem #3: The velocity of a particle in a gas is a random variable X with probability distribution fx (x) = 343 z2 e-7x x>0. The kinetic energy of the particle is Y = 2 mx2. Suppose that the mass of the particle is 16 yg. Find the probability distribution of Y. (Do not convert any units.) Enter your answer as a symbolic 343/16*sqrt(2*y/16)*(e^(-7*sqrt(2*) function of y, as in these examples Problem #3: 343 V (e-71 (20)/16) + e7V (2/16))...
Problem #4: Let 0 2 A = 2 9 and b = 0 2 4 Find the least squares solution of the linear system Ax = b. Enter the components of the least squares solution x = [x y]? into the answer box below (in order), separated with a comma. Problem #4: Enter your answer symbolically, as in these examples Just Save Submit Problem #4 for Grading Problem #4 Attempt #1 Attempt #2 Attempt #3 Your Answer: Your Mark:
Problem #2: Let y(t) be the solution to the following initial value problem 6, y'(0)3 y"7y Find Y(s), the Laplace transform ofy() Enter your answer as a symbolic function of s, as in these examples Problem #2: Submit Problem #2 for Grading Just Save Attempt #3 Problem #2 Attempt # 2 Attempt #5 Attempt#1 Attempt #4 Your Answer: Your Mark
4. Let X be a continuous exponentially distributed random variable with the intensity equal to 0.54. Find the probability that X takes of a value from interval (4, 8) thrice in 15 experiments. ir distrihiution laws:
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