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part a, b and c please Problem 4. (15 points) The probabiälity density function of X, the lifetime of a lamp (meured in i hours), Is given 10 0, s 10 (a) Find P(x>20) 3 b) What is the cumulativ...
2. The probability density function of X is given by 10 0,x < 10 a) Find...
2. The probability density function of X is given by 10 0,x < 10 a) Find P(X>20). b) What is the cumulative distribution function of X?
Problem No. 4 / 10 pts. Given The lifetime, in years, of a certain type of...
Problem No. 4 / 10 pts. Given The lifetime, in years, of a certain type of pump is a random variable with probability density function 0 True (a) What is the probability that a pump lasts more than 1 years? (b) What is the probability that a pump lasts between 2 and 4 years? (c) Find the mean lifetime (d) Find the variance of the lifetime. (e) Find the cumulative distribution function of the lifetime. (f) Find the median lifetime....
The distance X between trees in a given forest has a probability density function given f...
The distance X between trees in a given forest has a probability density function given f (x) cex/10, x >0, and zero otherwise with measurement in feet i) Find the value of c that makes this function a valid probability density function. [4 marks] ii) Find the cumulative distribution function (CDF) of X. 5 marks What is the probability that the distance from a randomly selected tree to its nearest neighbour is at least 15 feet. iii) 4 marks) iv)...
6. The probability density function of (lifetime of an electronic component in years) X is f, (x)...
6. The probability density function of (lifetime of an electronic component in years) X is f, (x)- 4 x exp(-r)U(x) 32 (a) What value of A will make this a valid pdf? (b) What is the probability that it will fail within 6 years, given that normally these units tend to fail within 4 to7 years? (c) What is P[IX-316)? (d) If the unit is known to fail within 6-8 years, what is the probability that it fail within 7...
please answer the last part "the probability that at least one out of 3 devices of...
please answer the last part "the probability that at least one
out of 3 devices of this type will function for at least 42
months:"
(1 point) The probability density function of X, the lifetime of a certain type of device (measured in months), is given by 0 if x s 15 f(x)= if x> 15 Find the following: P(X> 18) 5/6 The cumulative distribution function of X: 0 if xs 15 F(x) 15/x +1 if x> 15 The probability...
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...
Suppose that the probability distribution function for the life expectancy of a light bulb is giv...
Suppose that the probability distribution function for the life expectancy of a light bulb is given below. If a lamp has two light bulbs, what is the probability that they will both fail within the first 1000 hours (Hint: Assume one light bulb is X and the other Y. Since X and Yare independent events, assume,f(x,y)-NX)从Y ) where f-f.-f, then use problem #4 from Written Assignment #7 as a guide for the anti-differentiation.) f(x)=-1 е-(X-1000,2/125000 250 y2r
Suppose that the...
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...
Page (7) (10 points) The joint probability density function of X and Y is given by...
Page (7) (10 points) The joint probability density function of X and Y is given by a) Compute the marginal densities x and f b) Are X and Y independent? Why or why not? c) Compute P(Y > X7). MacBook Pro
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...
2. The probability density function of X is given by 10 0,x < 10 a) Find P(X>20). b) What is the cumulative distribution function of X?
Problem No. 4 / 10 pts. Given The lifetime, in years, of a certain type of pump is a random variable with probability density function 0 True (a) What is the probability that a pump lasts more than 1 years? (b) What is the probability that a pump lasts between 2 and 4 years? (c) Find the mean lifetime (d) Find the variance of the lifetime. (e) Find the cumulative distribution function of the lifetime. (f) Find the median lifetime....
The distance X between trees in a given forest has a probability density function given f (x) cex/10, x >0, and zero otherwise with measurement in feet i) Find the value of c that makes this function a valid probability density function. [4 marks] ii) Find the cumulative distribution function (CDF) of X. 5 marks What is the probability that the distance from a randomly selected tree to its nearest neighbour is at least 15 feet. iii) 4 marks) iv)...
6. The probability density function of (lifetime of an electronic component in years) X is f, (x)- 4 x exp(-r)U(x) 32 (a) What value of A will make this a valid pdf? (b) What is the probability that it will fail within 6 years, given that normally these units tend to fail within 4 to7 years? (c) What is P[IX-316)? (d) If the unit is known to fail within 6-8 years, what is the probability that it fail within 7...
please answer the last part "the probability that at least one
out of 3 devices of this type will function for at least 42
months:"
(1 point) The probability density function of X, the lifetime of a certain type of device (measured in months), is given by 0 if x s 15 f(x)= if x> 15 Find the following: P(X> 18) 5/6 The cumulative distribution function of X: 0 if xs 15 F(x) 15/x +1 if x> 15 The probability...
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...
Suppose that the probability distribution function for the life expectancy of a light bulb is given below. If a lamp has two light bulbs, what is the probability that they will both fail within the first 1000 hours (Hint: Assume one light bulb is X and the other Y. Since X and Yare independent events, assume,f(x,y)-NX)从Y ) where f-f.-f, then use problem #4 from Written Assignment #7 as a guide for the anti-differentiation.) f(x)=-1 е-(X-1000,2/125000 250 y2r
Suppose that the...
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...
Page (7) (10 points) The joint probability density function of X and Y is given by a) Compute the marginal densities x and f b) Are X and Y independent? Why or why not? c) Compute P(Y > X7). MacBook Pro
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...
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