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.
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Let X be an exponentially distributed random variable with
parameter value 2.
a) Use the...
a) Let T be an exponentially distributed random variable with parameter l= 1. Let U be...
a) Let T be an exponentially distributed random variable with parameter l= 1. Let U be a uniformly distributed random variable. Use inversion to show how to calculate samples {tı, t2, ..} from samples {U1, U2, ..} of U. b) Use any software of your choice to estimate by Monte Carlo simulation: E[sin(tanh, LT))
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...
3. Suppose that X and Y are independent exponentially distributed random variables with parameter λ, and...
3. Suppose that X and Y are independent exponentially distributed random variables with parameter λ, and further suppose that U is a uniformly distributed random variable between 0 and 1 that is independent from X and Y. Calculate Pr(X<U< Y) and estimate numerically (based on a visual plot, for example) the value of λ that maximizes this probability.
Let X be an exponentially distributed random variable with parameter λ. Prove that P(X > s...
Let X be an exponentially distributed random variable with parameter λ. Prove that P(X > s + tK > t) P(X > s) for any S,12 0
I. Let Y be an exponentially distributed random variable with parameter λ Compute the cdf and...
I. Let Y be an exponentially distributed random variable with parameter λ Compute the cdf and the pdf for the random variable X-e
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...
Let X be exponentially distributed with parameter 3. a) Compute P(X > 6 | X >...
Let X be exponentially distributed with parameter 3. a) Compute P(X > 6 | X > 2). b) Compute E(7e-12x+8+ 5). c) Let Y be independent from X. Suppose the PDF for Y is f(x) = 2x for 0 ≤ x ≤ 1 (and 0 else). Find the PDF of X + Y.
Problem 1 [20 points X is an exponentially distributed random variable with parameter A. a, b...
Problem 1 [20 points X is an exponentially distributed random variable with parameter A. a, b with b >a 0 are real numbers. Find PLX > E [a, b))
Problem #2: Let X be an exponentially distributed random variable with with 1 = . What...
Problem #2: Let X be an exponentially distributed random variable with with 1 = . What is Var(X)? Problem #2: Just Save Submit Problem #2 for Grading Attempt #1 | Attempt #2 | Attempt #3 Attempt #4 Attempt #5 Problem #2 Your Answer: Your Mark:
a) Let T be an exponentially distributed random variable with parameter l= 1. Let U be a uniformly distributed random variable. Use inversion to show how to calculate samples {tı, t2, ..} from samples {U1, U2, ..} of U. b) Use any software of your choice to estimate by Monte Carlo simulation: E[sin(tanh, LT))
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...
3. Suppose that X and Y are independent exponentially distributed random variables with parameter λ, and further suppose that U is a uniformly distributed random variable between 0 and 1 that is independent from X and Y. Calculate Pr(X<U< Y) and estimate numerically (based on a visual plot, for example) the value of λ that maximizes this probability.
Let X be an exponentially distributed random variable with parameter λ. Prove that P(X > s + tK > t) P(X > s) for any S,12 0
I. Let Y be an exponentially distributed random variable with parameter λ Compute the cdf and the pdf for the random variable X-e
Problem 1 [20 points X is an exponentially distributed random variable with parameter A. a, b with b >a 0 are real numbers. Find PLX > E [a, b))
Problem #2: Let X be an exponentially distributed random variable with with 1 = . What is Var(X)? Problem #2: Just Save Submit Problem #2 for Grading Attempt #1 | Attempt #2 | Attempt #3 Attempt #4 Attempt #5 Problem #2 Your Answer: Your Mark:
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