Let X be the lifetime of an electronic device. It is known that the average lifetime...
Please show all steps. The lifetime of an electronic device has a normal distribution with standard deviation 1.5 years. A random sample of 400 devices was drawn yielding the sample lifetime average of 6 years. a) Compute a 95% confidence interval for the mean lifetime of the electronic devices.
5. A light bulb has a lifetime that is exponentially distributed with rate parameter λ-5. Let L be a random variable denoting the sum of the lifetimes of 50 such bulbs. Assume that the bulbs are independent. (a) Compute E[L] and Var(L). b) Use the Central Limit Theorem to approximate P(8 < L < 12 ( ). (c) Use the Central Limit Theorem to find an interval (a,b), centered at ELLI, such that Pa KL b) 0.95. That is, your...
Let X be the lifetime of a certain type of electronic device (measured in hours). The probability density function of X is f(x) =10/x^2 , x > c 0, x ≤ c (a) Find the value of c that makes f(x) a legitimate pdf of X. (b) Compute P(X < 20).
The usable lifetime of a particular electronic component is known to follow an exponential distribution with a mean of 6.6 years. Let X = the usable lifetime of a randomly selected component. (a) The proportion of these components that have a usable lifetime between 5.9 and 8.1 years is . (b) The probability that a randomly selected component will have a usable life more than 7.5 years is . (c) The variance of X is
Problem 1 The pdf of X, the lifetime of a certain type of electronic device in hours, is given by if x > 10 10 if x < 10 f(x) = { ift 1. (1 point) Find the constant c that makes the a valid pdf. 2. (1 point) Find P(X > 20) 3. (1 point) Find F(x), i.e. the cummulative distribution of X? 4. (1 point) What is the median value of X?
An artide in the November 1983 Consumer Reports compared various types of batteries. The average lifetimes of Duracell Alkaline AA batteries and Eveready Energizer Alkaline AA batteries were given as 4.1 hours and 4.5 hours, respectively. Suppose these are the population average lifetimes. (a) LetW be the sample average lifetime of 114 Duracell and be the sample averege lifetime of 144 Evereatly Energizer batteries. What is the mean value of - (i..., where is the distribution of - centered)? Does...
: Let Yi, ½' . . . , Yn be an iid random sample from an exponential distribution with parameter where θ > 0. Here each Y, represents the lifetime of the ith battery, while θ represents the theoretical average lifetime. The pdf of each Y, is therefore given by fy (y) ei-1,2,...,n Consider the empirical average lifetime of the sample of n batteries given by Let a E R be a nonnegative real number. Consider the event A, defined...
please need a detailed answer! Thank you very much 28. An order of 4000 parts is received. Let random variable X be a number of defective parts. X follows a binomial distribution with n 4000, p .005. Using the central limit theorem, [normal approximation) a) find the probabilities : P(18 <X <21), P (X > 21) b) find the probability that average number of defective parts in 36 randomly chosen parts exceeds 21. c) Why is it possible to apply...
Let x represent the dollar amount spent on supermarket impulse buying in a 10-minute (unplanned) shopping interval. Based on a certain article, the mean of the x distribution is about $21 and the estimated standard deviation is about $9. (a) Consider a random sample of n = 40 customers, each of whom has 10 minutes of unplanned shopping time in a supermarket. From the central limit theorem, what can you say about the probability distribution of x, the average amount...
Let x represent the dollar amount spent on supermarket impulse buying in a 10-minute (unplanned) shopping interval. Based on a certain article, the mean of the x distribution is about $30 and the estimated standard deviation is about $5. (a) Consider a random sample of n = 40 customers, each of whom has 10 minutes of unplanned shopping time in a supermarket. From the central limit theorem, what can you say about the probability distribution of x, the average amount...