Question: please help me with this problem in the probability. i find it very difficult so i need help 5. Suppose a lightbulb has a lifetime

please help me with this problem in the probability. i find it very difficult so i need help

5. Suppose a lightbulb has a lifetime X that is exponentially distributed with mean 300 hours. (a) What is the probability the bulb lasts longer than 400 hours? (b) What is the standard deviation for the lifetime of the bulb? (c) What is the median of the lightbulb's distribution? (d) Given that the bulb has lasted over 260 hours, what is the probability it will last over 420 hours? (e) Suppose the bulb will be replaced once the bulb goes out or once the bulb's lifetime has reached 500 hours (whichever happens rst). Let Y be the time of the bulb's replacement. What is E (Y)? (f) Refer to (e). Suppose for each hour the bulb is on, it costs $25. Addi tionally, it costs $10 to install the bulb. Again let Y be the time of the bulb's replacement. What is the expected cost to maintain the rst bulb? (g) Refer to (e). What is E ()? (h) What is Var (X100)

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

PLEASE READ THE QUESTION CAREFULLY. I don't want answer with the results: 1/2 and 1/3 since there are no specific numbers given here. The coin is flipped n times This is my third time positing this...

Hi! Please help me solve this problem, Thanks! Suppose that X1, #2 and variance 0 (a) Find a} 7 )7). (b) 2 1\"] _ #2 Find in} 7 l7). 2 X . .. X and Y Y . . 2. . m 1, 2. 2. The difference between the...

Please help me with this question, its been hard to find someone to help: Suppose that survival lifetime 7 has the Geometric distribution P(T = x) = (1 - 1)*-1, for x = 1,2, .... with 0 x) defines...

Topic: Bayesian inference. Estimating the parameter of a geometric r.v. Problem 6. Determining the type of a lightbulb 3 points possible (graded) The lifetime of a type-A bulb is exponentially...

1. A player throws a fair die and simultaneously flips a fair coin. If the coin lands heads, then she wins twice, and if tails, then one-half of the value that appears on the die. Determine her...

Please help me with my macro quiz Problem 2: A two-server queueing system is in a steady-state condition and the steady state probabilities are po = 16: P1 = 16 : P2 = 16:P3 = 16 . PA = 16: Pn = 0 if...

Directions: Solve each word problem. Provide the given values. Show the conversion of raw score to z-score (3 points per item ). Illustrate the appropriate shading of the normal curve for each...

1sp(z>123) 1&P(135 15. P (z > 1.23) 16. P 17. P ( 1.46

please help me out The number of births in September is modeled by a Poisson random variable T with parameter , which represents the expected number of births. Suppose that one uses T to test the...

Calculation the kinetic energy and momentum of a proton (mo = 1.67 X 10-27Kg) traveling 7.35 X 107 m/s. by what percentage would your calculation have been in error if you had use classical formula?

What should the writer strive to do in the body of a formal report?

Agnes deposited R100 000 in an account earning 9,71% per year, compounded quarterly. After four years she decided to deposit an additional R12 000 in this account every three months. If the interest...

Cost Information and FIFO Gunnison Company had the following equivalent units schedule and cost information for its Sewing Department for the month of December: Direct Materials Conversion Costs...