suppose that the lifetime in years of a particular brand of fuse can be described by...
Homework Answers
Probability that the system is still functioning after time t is computed as the probability that all 3 of the fuses are still working after time t, this is because they are connected in series and all of them should work for the whole thing to work
Therefore the required probability here is computed as:
Therefore the required probability here is given as:
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suppose that the lifetime in years of a particular brand of fuse
can be described by...
please show work 5. (15 points) Each of two lightbulbs have lifetime (measured in thous ands...
please show work
5. (15 points) Each of two lightbulbs have lifetime (measured in thous ands of hours) with an exponential distribution with parameter = 1. These lifetimes X and Y are independent. Set up an integration for the probability that the total lifetime of the two bulbs is at most 2. Don't do the integral. (Hint: draw a picture of the region where x 2 0, y 2 0 and ax+y< 2.) probability that at least 6. Widget makers...
Make sure to use double integral formula since the question asks for it. Thanks The probability...
Make sure to use double
integral formula since the question asks for it. Thanks
The probability density function of an exponentially distributed random variable with mean 1/λ is λ e-At for t > 0. Suppose the lifetime of a particular brand of light bulb follows an exponential distribution with a mean of 1000 hours. If a light fixture is equipped with two such bulbs, then what is the probability that it still illuminates a room after 1000 hours? Develop your...
The probability density function of an exponentially distributed random variable with mean 1/λ is λe^−λt for...
The probability density function of an exponentially distributed random variable with mean 1/λ is λe^−λt for t≥0. Suppose the lifetime of a particular brand of light bulb follows an exponential distribution with a mean of 1000 hours. If a light fixture is equipped with two such bulbs, then what is the probability that it still illuminates a room after 1000 hours? Develop your answer by evaluating a double integral. What assumption must you make about the respective lifetimes of the...
The probability density function of an exponentially distributed random variable with mean 1/λ is λe^−λt for...
The probability density function of an exponentially distributed random variable with mean 1/λ is λe^−λt for t≥0. Suppose the lifetime of a particular brand of light bulb follows an exponential distribution with a mean of 1000 hours. If a light fixture is equipped with two such bulbs, then what is the probability that it still illuminates a room after 1000 hours? Develop your answer by evaluating a double integral. What assumption must you make about the respective lifetimes of the...
(12 points) Consider the system comprised of three components as shown below. Suppose The lifetime of...
(12 points) Consider the system comprised of three components as shown below. Suppose The lifetime of Component 1 is exponentially-distributed with parameter 11 = 1/10. • The lifetime of Component 2 is exponentially-distributed with parameter 12 = 1/20. • The lifetime of Component 3 is exponentially-distributed with parameter 13 = 1/15. The system is working if both (A) Component 1 is working, and (B) Component 2 or/and Component 3 is working. Compute the probability that the system is still working...
Suppose a system of ive components Ai,1 Si S 5 is arranged as follows 2 Assum e the lifetime of each component is exponentially distributed with parameter) and the components function independently....
Suppose a system of ive components Ai,1 Si S 5 is arranged as follows 2 Assum e the lifetime of each component is exponentially distributed with parameter) and the components function independently. Let of the i-th component, that is the random variable defined by (Xi - t) means that the the i-th component stops working at time t. Saying that Xi has an exponenti distribution with parameter X means X, be the lifetime random variable and P(Xi s t)-1-e*. be...
I can do the first part of the question 1a, could someone show me step by...
I can do the first part of the question 1a, could
someone show me step by step how to do do 1b?
) Y.Ya..., Y, form a random sample from a probability distribution with cumu- lative distribution function Fy (u) and probability density function fr(u). Let Write the cumulative distribution function for Ya) in terms of Fy(y) and hence show that the probability density function for Yy is fy(1)(y) = n(1-Fr (v))"-ify(y). [8 marks] (b) An engineering system consists of...
Prove that Box-Muller method described in class generates independent standard normal random variables. 4 a) Prove...
Prove that Box-Muller method described in class generates
independent standard normal random variables.
4 a) Prove that the Box-Muller method described in class generates independent standard ll generate n to write a function which wi σ-) random variables b) Suppose that X is an exponential random variable with rate parameter λ and that Y is the integer part of X. Show that Y has a geometric distribution and use this result to give an algorithm to generate a random sample...
Consider a system consisting of three components as pictured. The system will continue to function as...
Consider a system consisting of three components as pictured. The system will continue to function as long as the first component functions and either component 2 or component 3 functions. Let X1, X2, and X3 denote the lifetimes of components 1, 2, and 3, respectively. Suppose the Xi's are independent of one another and each X, has an exponential distribution with parameter λ. (a) Let Y denote the system lifetime. Obtain the cumulative distribution function of Y and differentiate to...
4 a) Prove that the Box-Muller method described in class generates independent standard ll generate n...
4 a) Prove that the Box-Muller method described in class generates independent standard ll generate n to write a function which wi σ-) random variables b) Suppose that X is an exponential random variable with rate parameter λ and that Y is the integer part of X. Show that Y has a geometric distribution and use this result to give an algorithm to generate a random sample of size n from the geometric distribution with specified success probability p implementing...
please show work
5. (15 points) Each of two lightbulbs have lifetime (measured in thous ands of hours) with an exponential distribution with parameter = 1. These lifetimes X and Y are independent. Set up an integration for the probability that the total lifetime of the two bulbs is at most 2. Don't do the integral. (Hint: draw a picture of the region where x 2 0, y 2 0 and ax+y< 2.) probability that at least 6. Widget makers...
Make sure to use double
integral formula since the question asks for it. Thanks
The probability density function of an exponentially distributed random variable with mean 1/λ is λ e-At for t > 0. Suppose the lifetime of a particular brand of light bulb follows an exponential distribution with a mean of 1000 hours. If a light fixture is equipped with two such bulbs, then what is the probability that it still illuminates a room after 1000 hours? Develop your...
(12 points) Consider the system comprised of three components as shown below. Suppose The lifetime of Component 1 is exponentially-distributed with parameter 11 = 1/10. • The lifetime of Component 2 is exponentially-distributed with parameter 12 = 1/20. • The lifetime of Component 3 is exponentially-distributed with parameter 13 = 1/15. The system is working if both (A) Component 1 is working, and (B) Component 2 or/and Component 3 is working. Compute the probability that the system is still working...
Suppose a system of ive components Ai,1 Si S 5 is arranged as follows 2 Assum e the lifetime of each component is exponentially distributed with parameter) and the components function independently. Let of the i-th component, that is the random variable defined by (Xi - t) means that the the i-th component stops working at time t. Saying that Xi has an exponenti distribution with parameter X means X, be the lifetime random variable and P(Xi s t)-1-e*. be...
I can do the first part of the question 1a, could
someone show me step by step how to do do 1b?
) Y.Ya..., Y, form a random sample from a probability distribution with cumu- lative distribution function Fy (u) and probability density function fr(u). Let Write the cumulative distribution function for Ya) in terms of Fy(y) and hence show that the probability density function for Yy is fy(1)(y) = n(1-Fr (v))"-ify(y). [8 marks] (b) An engineering system consists of...
Prove that Box-Muller method described in class generates
independent standard normal random variables.
4 a) Prove that the Box-Muller method described in class generates independent standard ll generate n to write a function which wi σ-) random variables b) Suppose that X is an exponential random variable with rate parameter λ and that Y is the integer part of X. Show that Y has a geometric distribution and use this result to give an algorithm to generate a random sample...
Consider a system consisting of three components as pictured. The system will continue to function as long as the first component functions and either component 2 or component 3 functions. Let X1, X2, and X3 denote the lifetimes of components 1, 2, and 3, respectively. Suppose the Xi's are independent of one another and each X, has an exponential distribution with parameter λ. (a) Let Y denote the system lifetime. Obtain the cumulative distribution function of Y and differentiate to...
4 a) Prove that the Box-Muller method described in class generates independent standard ll generate n to write a function which wi σ-) random variables b) Suppose that X is an exponential random variable with rate parameter λ and that Y is the integer part of X. Show that Y has a geometric distribution and use this result to give an algorithm to generate a random sample of size n from the geometric distribution with specified success probability p implementing...
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