The lifetime T , in years, of the light bulb you just purchased satisfies P(T >...
The lifetime T , in years, of the light bulb you just purchased satisfies
P(T > t) = e^(−t/4) for all t ≥ 0.
Suppose the bulb has lasted more than x years, where x ≥ 0. Given this information, what’s the conditional probability that it will last at most x + 1 years? Does your answer depend on the value of x?
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The lifetime T , in years, of the light bulb you just purchased
satisfies
P(T >...
6. Assume that the lifetime of a light bulb is 5X years where X is a...
6. Assume that the lifetime of a light bulb is 5X years where X is a random variable with the density function if 1 2, otherwise 0, f(x) (a) What fraction of light bulbs last less than 7.5 years? (b) What fraction of light bulbs that last less than 7.5 years lasted between 5 and 6.25 years?
1. Suppose that the longevity of a light bulb is exponential with a mean lifetime of...
1. Suppose that the longevity of a light bulb is exponential with a mean lifetime of eight years. Find the probability that a light bulb lasts between 6 and 8 years. a. 0.875 b. 0.125 c. 0.896 d. 0.104 2. At a 911 call center, calls come in at an average rate of one call every two minutes. Assume that the time that elapses from one call to the next has the exponential distribution. Find the probability after a call is...
2. Light bulbs are known to have an average lifetime of 2,000 hours. Suppose we model...
2. Light bulbs are known to have an average lifetime of 2,000 hours. Suppose we model the lifetime of a light bulb by the following probability density function with (yet unknown) parameter c: p(t) = 1-e-t/c when t20 and p(t) = 0 otherwise. (a) Determine the value of the parameter c so that the probability density function has mean 2,000 hours. (b) Determine the probability a lightbulb fails before 1,500 hours. (C) Suppose the lightbulb has already been on for...
Suppose the manufacturer claims that the mean lifetime of a light bulb is more than 10,000...
Suppose the manufacturer claims that the mean lifetime of a light bulb is more than 10,000 hours. In a sample of 30 light bulbs, it was found that they only last 9,900 hours on average. Assume the population standard deviation is 120 hours. At 0.05 significance level, can we reject the claim by the manufacturer? Select one: a. We reject the claim b. We accept the claim
5) You purchase a certain product. The manual states that the lifetime T of the product,...
5) You purchase a certain product. The manual states that the lifetime T of the product, defined as the amount of time (in years) the product works properly until it breaks down, satisfies P(T > t) = { $, for all t > 0. For example, the probability that the product lasts more than (or equal to) 2 years is P(T > 2) = e Ğ = 0.6703. I purchase the product and use it for two years without any...
(Sec. 4.3) An average light bulb manufactured at The Lightbulb Company lasts and average of 300...
(Sec. 4.3) An average light bulb manufactured at The Lightbulb Company lasts and average of 300 days, with a standard deviation of 50 days. Suppose the lifespan of a light bulb from this company is normally distributed. (a) What is the probability that a light bulb from this company lasts less than 210 days? More than 330 days? (b) What is the probability that a light bulb from this company lasts between 280 and 380 days? (c) How would you...
4. A company tells you that their light bulbs last two years on average, with an...
4. A company tells you that their light bulbs last two years on average, with an exponential distribution. a. If they are correct, what is the probability that the light bulb will last between three and four years? b. What is the probability that the light bulb will last one year or less? c. If the light bulb lasts eight years, should you be surprised? (Is the probability of this event less than five percent?) Does it seem like the...
I just need help with (c) please. (2+3+5 pts.) The life X (in years) of a...
I just need help with (c) please.
(2+3+5 pts.) The life X (in years) of a regulator of a car has the pdf 2 1 Car 3.x2 (3/8)3 83 e 0 < x < 0. (a) What is the probability that this regulator will last at least 5 years? (b) Given that it has lasted at least 5 years, what is the conditional probability that it will last at least another 5 years? (c) Suppose the replacement cost Y (in...
The lifetime, in years, of a certain type of pump is a random variable with probability...
The lifetime, in years, of a certain type of pump is a random variable with probability density function x 20 (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 the...
The life X (in years) of a regulator of a car has the pdf 32 f(3)...
The life X (in years) of a regulator of a car has the
pdf
32 f(3) = 83 -e-(2/8), 0<x< 0. (a) What is the probability that this regulator will last at least 5 years? (b) Given that it has lasted at least 5 years, what is the conditional probability that it will last at least another 5 years? (c) Suppose the replacement cost Y in dollars) after the regular dies is proportional to X and with mean $5,120. Find...
6. Assume that the lifetime of a light bulb is 5X years where X is a random variable with the density function if 1 2, otherwise 0, f(x) (a) What fraction of light bulbs last less than 7.5 years? (b) What fraction of light bulbs that last less than 7.5 years lasted between 5 and 6.25 years?
2. Light bulbs are known to have an average lifetime of 2,000 hours. Suppose we model the lifetime of a light bulb by the following probability density function with (yet unknown) parameter c: p(t) = 1-e-t/c when t20 and p(t) = 0 otherwise. (a) Determine the value of the parameter c so that the probability density function has mean 2,000 hours. (b) Determine the probability a lightbulb fails before 1,500 hours. (C) Suppose the lightbulb has already been on for...
5) You purchase a certain product. The manual states that the lifetime T of the product, defined as the amount of time (in years) the product works properly until it breaks down, satisfies P(T > t) = { $, for all t > 0. For example, the probability that the product lasts more than (or equal to) 2 years is P(T > 2) = e Ğ = 0.6703. I purchase the product and use it for two years without any...
(Sec. 4.3) An average light bulb manufactured at The Lightbulb Company lasts and average of 300 days, with a standard deviation of 50 days. Suppose the lifespan of a light bulb from this company is normally distributed. (a) What is the probability that a light bulb from this company lasts less than 210 days? More than 330 days? (b) What is the probability that a light bulb from this company lasts between 280 and 380 days? (c) How would you...
4. A company tells you that their light bulbs last two years on average, with an exponential distribution. a. If they are correct, what is the probability that the light bulb will last between three and four years? b. What is the probability that the light bulb will last one year or less? c. If the light bulb lasts eight years, should you be surprised? (Is the probability of this event less than five percent?) Does it seem like the...
I just need help with (c) please.
(2+3+5 pts.) The life X (in years) of a regulator of a car has the pdf 2 1 Car 3.x2 (3/8)3 83 e 0 < x < 0. (a) What is the probability that this regulator will last at least 5 years? (b) Given that it has lasted at least 5 years, what is the conditional probability that it will last at least another 5 years? (c) Suppose the replacement cost Y (in...
The lifetime, in years, of a certain type of pump is a random variable with probability density function x 20 (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 the...
The life X (in years) of a regulator of a car has the
pdf
32 f(3) = 83 -e-(2/8), 0<x< 0. (a) What is the probability that this regulator will last at least 5 years? (b) Given that it has lasted at least 5 years, what is the conditional probability that it will last at least another 5 years? (c) Suppose the replacement cost Y in dollars) after the regular dies is proportional to X and with mean $5,120. Find...
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