What is the median lifetime of the light bulbs

Assignment Help Mathematics

Reference no: EM131015378

1. Let f(x) = k(3x - x²) if 0 ≤ x ≤ 3 and f(x) = 0 if x < 0 or x > 3.

a. For what value of k is f a probability density function?

b. For that value of k, find P(X > 1). (c), Find the mean.

2. a. A type of light bulb is labeled as having an average lifetime of 1000 hours. It's reasonable to model the probability of failure of these bulbs by an exponential density function with mean µ = 1000. Use this model to find the probability that a bulb (i) fails within the first 200 hours, (ii) burns for more than 800 hours.

b. What is the median lifetime of these light bulbs? Problem description: #2, sketch the curve by using the parametric equations to plot points. Indicate with an arrow the direction in which the curve is traced as t increases. x = t³ + t, y = t² + 2, -2 ≤ t ≤ 2.

3. a. Sketch the curve by using the parametric equations to plot points. Indicate with an arrow the direction in which the curve is traced as t increases.

b. Eliminate the parameter to find a Cartesian equation of the curve. x = 3t + 2, y = 2t + 3.

4. a. Eliminate the parameter to find a Cartesian equation of the curve.

b. Sketch the curve and indicate with an arrow the direction in which the curve is traced as the parameter increases. x = 12 cos θ, y = 2 sin θ, 0 ≤ θ ≤ π.

Reference no: EM131015378

Questions Cloud

What do you believe is the main theme jesus is communicating : Read the parable of the Prodigal Son (Luke 15:11-32) and answer the following questions: What do you believe is the main theme Jesus is communicating?

What would you recommend and why : What would you recommend and why? Would your recommendations differ if the therapy had concluded? Would your recommendations differ depending on the type of mental health professional involved? If yes, in what way? If no, why not

What are the ethical issues involved in a duty to protect : What are the ethical issues involved in a duty to protect? Explain using the above scenario and discuss variations to the scenario that might lead you to a different ethical decision

Discuss the issues pertaining to informed consent : In this assignment, you will discuss the issues pertaining to informed consent in conducting evaluations and apply ethical decision making to a scenario in which there is a professional ethical conflict

What is the median lifetime of the light bulbs : What is the median lifetime of these light bulbs? Problem description: #2, sketch the curve by using the parametric equations to plot points. Indicate with an arrow the direction in which the curve is traced as t increases.

How do violent video games impact adolescents : How does a balanced calendar affect the academic grade point average of public-school students in grade nine?

Implement the data modelling for a database : Implement the data modelling for a database that is based on the given application scenario - design and implement The Best Home business database

How that contribution changed the field of economics : explore how meaningful his ideas might be to our understanding of the world

Accepting the merger agreement : How much money can Toys R Us save in present value terms by accepting the merger agreement if we assume a 10% cost of capital?

User Account

All Pages